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class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Conteúdo" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Conteúdo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ocultar</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Início</div> </a> </li> <li id="toc-Sobre_os_divisores" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sobre_os_divisores"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Sobre os divisores</span> </div> </a> <ul id="toc-Sobre_os_divisores-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Conteúdo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Índice" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Alternar o índice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Alternar o índice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Divisor</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir para um artigo noutra língua. Disponível em 65 línguas" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-65" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">65 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/D%C7%A3lere" title="Dǣlere — inglês antigo" lang="ang" hreflang="ang" data-title="Dǣlere" data-language-autonym="Ænglisc" data-language-local-name="inglês antigo" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D8%B3%D9%85_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="قاسم (رياضيات) — árabe" lang="ar" hreflang="ar" data-title="قاسم (رياضيات)" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Lakiri" title="Lakiri — aimará" lang="ay" hreflang="ay" data-title="Lakiri" data-language-autonym="Aymar aru" data-language-local-name="aimará" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D0%B7%D1%8F%D0%BB%D1%96%D0%BC%D0%B0%D1%81%D1%86%D1%8C" title="Дзялімасць — bielorrusso" lang="be" hreflang="be" data-title="Дзялімасць" data-language-autonym="Беларуская" data-language-local-name="bielorrusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%94%D0%B7%D0%B5%D0%BB%D1%8C%D0%BD%D1%96%D0%BA" title="Дзельнік — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Дзельнік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%89%E0%A7%8E%E0%A6%AA%E0%A6%BE%E0%A6%A6%E0%A6%95_(%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4)" title="উৎপাদক (গণিত) — bengalês" lang="bn" hreflang="bn" data-title="উৎপাদক (গণিত)" data-language-autonym="বাংলা" data-language-local-name="bengalês" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Divisor" title="Divisor — catalão" lang="ca" hreflang="ca" data-title="Divisor" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%95%D8%B4%D8%AF%D8%B1%D8%A7%D9%88" title="بەشدراو — curdo central" lang="ckb" hreflang="ckb" data-title="بەشدراو" data-language-autonym="کوردی" data-language-local-name="curdo central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/D%C4%9Blitelnost" title="Dělitelnost — checo" lang="cs" hreflang="cs" data-title="Dělitelnost" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D0%B0%D0%B9%D0%BB%D0%B0%D0%BD%D0%B0%D1%81%D0%BB%C4%83%D1%85" title="Пайланаслăх — chuvash" lang="cv" hreflang="cv" data-title="Пайланаслăх" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Divisor" title="Divisor — dinamarquês" lang="da" hreflang="da" data-title="Divisor" data-language-autonym="Dansk" data-language-local-name="dinamarquês" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CE%B9%CF%81%CE%AD%CF%84%CE%B7%CF%82" title="Διαιρέτης — grego" lang="el" hreflang="el" data-title="Διαιρέτης" data-language-autonym="Ελληνικά" data-language-local-name="grego" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Divisor" title="Divisor — inglês" lang="en" hreflang="en" data-title="Divisor" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Divizoro" title="Divizoro — esperanto" lang="eo" hreflang="eo" data-title="Divizoro" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Divisibilidad" title="Divisibilidad — espanhol" lang="es" hreflang="es" data-title="Divisibilidad" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zatitzaile" title="Zatitzaile — basco" lang="eu" hreflang="eu" data-title="Zatitzaile" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%82%D8%B3%D9%88%D9%85%E2%80%8C%D8%B9%D9%84%DB%8C%D9%87" title="مقسوم‌علیه — persa" lang="fa" hreflang="fa" data-title="مقسوم‌علیه" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Jaollisuus" title="Jaollisuus — finlandês" lang="fi" hreflang="fi" data-title="Jaollisuus" data-language-autonym="Suomi" data-language-local-name="finlandês" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Divisor" title="Divisor — fijiano" lang="fj" hreflang="fj" data-title="Divisor" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijiano" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Diviseur" title="Diviseur — francês" lang="fr" hreflang="fr" data-title="Diviseur" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Divisor" title="Divisor — galego" lang="gl" hreflang="gl" data-title="Divisor" data-language-autonym="Galego" data-language-local-name="galego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%85%E0%AA%B5%E0%AA%AF%E0%AA%B5" title="અવયવ — guzerate" lang="gu" hreflang="gu" data-title="અવયવ" data-language-autonym="ગુજરાતી" data-language-local-name="guzerate" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%97%D7%9C%D7%A7" title="מחלק — hebraico" lang="he" hreflang="he" data-title="מחלק" data-language-autonym="עברית" data-language-local-name="hebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AD%E0%A4%BE%E0%A4%9C%E0%A4%95" title="भाजक — hindi" lang="hi" hreflang="hi" data-title="भाजक" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Djelitelj" title="Djelitelj — croata" lang="hr" hreflang="hr" data-title="Djelitelj" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Oszthat%C3%B3s%C3%A1g" title="Oszthatóság — húngaro" lang="hu" hreflang="hu" data-title="Oszthatóság" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%A1%D5%AA%D5%A1%D5%B6%D5%A5%D5%AC%D5%AB%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Բաժանելիություն — arménio" lang="hy" hreflang="hy" data-title="Բաժանելիություն" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pembagi" title="Pembagi — indonésio" lang="id" hreflang="id" data-title="Pembagi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Dividanto" title="Dividanto — ido" lang="io" hreflang="io" data-title="Dividanto" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%9E%C3%A1ttur_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Þáttur (stærðfræði) — islandês" lang="is" hreflang="is" data-title="Þáttur (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="islandês" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Divisore" title="Divisore — italiano" lang="it" hreflang="it" data-title="Divisore" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B4%84%E6%95%B0" title="約数 — japonês" lang="ja" hreflang="ja" data-title="約数" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B%D1%81%D1%8B%D0%B7_%D0%B1%D3%A9%D0%BB%D1%96%D0%BD%D0%B3%D1%96%D1%88%D1%82%D1%96%D0%BA_%D0%B1%D0%B5%D0%BB%D0%B3%D1%96%D1%81%D1%96" title="Қалдықсыз бөлінгіштік белгісі — cazaque" lang="kk" hreflang="kk" data-title="Қалдықсыз бөлінгіштік белгісі" data-language-autonym="Қазақша" data-language-local-name="cazaque" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%BD%EC%88%98" title="약수 — coreano" lang="ko" hreflang="ko" data-title="약수" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Deeler" title="Deeler — luxemburguês" lang="lb" hreflang="lb" data-title="Deeler" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburguês" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Dal%C4%ABt%C4%81js" title="Dalītājs — letão" lang="lv" hreflang="lv" data-title="Dalītājs" data-language-autonym="Latviešu" data-language-local-name="letão" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D1%82%D0%B5%D0%BB" title="Делител — macedónio" lang="mk" hreflang="mk" data-title="Делител" data-language-autonym="Македонски" data-language-local-name="macedónio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%BE%E0%A4%9C%E0%A4%95_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="विभाजक (गणित) — marata" lang="mr" hreflang="mr" data-title="विभाजक (गणित)" data-language-autonym="मराठी" data-language-local-name="marata" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Faktor_(matematik)" title="Faktor (matematik) — malaio" lang="ms" hreflang="ms" data-title="Faktor (matematik)" data-language-autonym="Bahasa Melayu" data-language-local-name="malaio" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Divider" title="Divider — maltês" lang="mt" hreflang="mt" data-title="Divider" data-language-autonym="Malti" data-language-local-name="maltês" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%86%E1%80%81%E1%80%BD%E1%80%B2%E1%80%80%E1%80%AD%E1%80%94%E1%80%BA%E1%80%B8" title="ဆခွဲကိန်း — birmanês" lang="my" hreflang="my" data-title="ဆခွဲကိန်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmanês" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Deler" title="Deler — neerlandês" lang="nl" hreflang="nl" data-title="Deler" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Faktor_i_matematikk" title="Faktor i matematikk — norueguês nynorsk" lang="nn" hreflang="nn" data-title="Faktor i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norueguês nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dzielnik" title="Dzielnik — polaco" lang="pl" hreflang="pl" data-title="Dzielnik" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Divizor" title="Divizor — romeno" lang="ro" hreflang="ro" data-title="Divizor" data-language-autonym="Română" data-language-local-name="romeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" title="Делимость — russo" lang="ru" hreflang="ru" data-title="Делимость" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Djeljivost" title="Djeljivost — servo-croata" lang="sh" hreflang="sh" data-title="Djeljivost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="servo-croata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Divisor" title="Divisor — Simple English" lang="en-simple" hreflang="en-simple" data-title="Divisor" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Delite%C4%BE" title="Deliteľ — eslovaco" lang="sk" hreflang="sk" data-title="Deliteľ" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Delitelj" title="Delitelj — esloveno" lang="sl" hreflang="sl" data-title="Delitelj" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%B5%D1%99%D0%B8%D0%B2%D0%BE%D1%81%D1%82" title="Дељивост — sérvio" lang="sr" hreflang="sr" data-title="Дељивост" data-language-autonym="Српски / srpski" data-language-local-name="sérvio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Delbarhet" title="Delbarhet — sueco" lang="sv" hreflang="sv" data-title="Delbarhet" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Tajlowalno%C5%9B%C4%87" title="Tajlowalność — silesiano" lang="szl" hreflang="szl" data-title="Tajlowalność" data-language-autonym="Ślůnski" data-language-local-name="silesiano" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%95%E0%AF%81%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="வகுஎண் — tâmil" lang="ta" hreflang="ta" data-title="வகுஎண்" data-language-autonym="தமிழ்" data-language-local-name="tâmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B0%BE%E0%B0%B0%E0%B0%A3%E0%B0%BE%E0%B0%82%E0%B0%95%E0%B0%AE%E0%B1%81" title="కారణాంకము — telugu" lang="te" hreflang="te" data-title="కారణాంకము" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%AB%E0%B8%B2%E0%B8%A3" title="ตัวหาร — tailandês" lang="th" hreflang="th" data-title="ตัวหาร" data-language-autonym="ไทย" data-language-local-name="tailandês" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/B%C3%B6len" title="Bölen — turco" lang="tr" hreflang="tr" data-title="Bölen" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B4%D1%96%D0%BB%D1%8C%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Подільність — ucraniano" lang="uk" hreflang="uk" data-title="Подільність" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Bo%CA%BBlinishlik" title="Boʻlinishlik — usbeque" lang="uz" hreflang="uz" data-title="Boʻlinishlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeque" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Chia_h%E1%BA%BFt" title="Chia hết — vietnamita" lang="vi" hreflang="vi" data-title="Chia hết" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BA%A6%E6%95%B0" title="约数 — wu" lang="wuu" hreflang="wuu" data-title="约数" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9B%A0%E6%95%B8" title="因數 — chinês" lang="zh" hreflang="zh" data-title="因數" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%9B%A0%E6%95%B8" title="因數 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="因數" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Iok-s%C3%B2%CD%98" title="Iok-sò͘ — min nan" lang="nan" hreflang="nan" data-title="Iok-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9B%A0%E6%95%B8" title="因數 — cantonês" lang="yue" hreflang="yue" data-title="因數" data-language-autonym="粵語" data-language-local-name="cantonês" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q50708#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espaços nominais"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Divisor" title="Ver a página de conteúdo [c]" accesskey="c"><span>Artigo</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discuss%C3%A3o:Divisor" rel="discussion" title="Discussão sobre o conteúdo da página [t]" accesskey="t"><span>Discussão</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Mudar a variante da língua" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">português</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Vistas"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Divisor"><span>Ler</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Divisor&veaction=edit" title="Editar esta página [v]" accesskey="v"><span>Editar</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Divisor&action=edit" title="Editar o código-fonte desta página [e]" accesskey="e"><span>Editar código-fonte</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Divisor&action=history" title="Edições anteriores desta página. [h]" accesskey="h"><span>Ver histórico</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Ferramentas de página"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Ferramentas" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Ferramentas</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Ferramentas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Mais opções" > <div class="vector-menu-heading"> Operações </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Divisor"><span>Ler</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Divisor&veaction=edit" title="Editar esta página [v]" accesskey="v"><span>Editar</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Divisor&action=edit" title="Editar o código-fonte desta página [e]" accesskey="e"><span>Editar código-fonte</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Divisor&action=history"><span>Ver histórico</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Geral </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginas_afluentes/Divisor" title="Lista de todas as páginas que contêm hiperligações para esta [j]" accesskey="j"><span>Páginas afluentes</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Altera%C3%A7%C3%B5es_relacionadas/Divisor" rel="nofollow" title="Mudanças recentes nas páginas para as quais esta contém hiperligações [k]" accesskey="k"><span>Alterações relacionadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="//pt.wikipedia.org/wiki/Wikipedia:Carregar_ficheiro" title="Carregar ficheiros [u]" accesskey="u"><span>Carregar ficheiro</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Divisor&oldid=64191748" title="Hiperligação permanente para esta revisão desta página"><span>Hiperligação permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Divisor&action=info" title="Mais informações sobre esta página"><span>Informações da página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Divisor&id=64191748&wpFormIdentifier=titleform" title="Informação sobre como citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlShortener&url=https%3A%2F%2Fpt.wikipedia.org%2Fwiki%2FDivisor"><span>Obter URL encurtado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fpt.wikipedia.org%2Fwiki%2FDivisor"><span>Descarregar código QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimir/exportar </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Especial:Livro&bookcmd=book_creator&referer=Divisor"><span>Criar um livro</span></a></li><li id="coll-download-as-rl" 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class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Origem: Wikipédia, a enciclopédia livre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="pt" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r68971778">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output 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.tmbox-move{border:2px solid #9932cc}.mw-parser-output .tmbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .tmbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .tmbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .tmbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .tmbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .tmbox{margin:4px 10%}.mw-parser-output .tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="box-Mais_notas plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Ficheiro:Question_book-new.svg" class="mw-file-description"><img alt="Esta página cita fontes, mas não cobrem todo o conteúdo" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Esta página <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">cita fontes</a>, mas que <b><a href="/wiki/Wikip%C3%A9dia:V" class="mw-redirect" title="Wikipédia:V">não cobrem</a> todo o conteúdo</b>.<span class="hide-when-compact"> Ajude a <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Refer%C3%AAncias_e_notas_de_rodap%C3%A9" title="Wikipédia:Livro de estilo/Referências e notas de rodapé">inserir referências</a> (<small><i>Encontre fontes:</i> <span class="plainlinks"><a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/">ABW</a>  •  <a rel="nofollow" class="external text" href="https://www.periodicos.capes.gov.br">CAPES</a>  •  <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&as_epq=Divisor">Google</a> (<a rel="nofollow" class="external text" href="https://www.google.com/search?hl=pt&tbm=nws&q=Divisor&oq=Divisor">notícias</a> • <a rel="nofollow" class="external text" href="http://books.google.com/books?&as_brr=0&as_epq=Divisor">livros</a> • <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?hl=pt&q=Divisor">acadêmico</a>)</span></small>).</span> <small class="date-container"><i>(<span class="date">Julho de 2017</span>)</i></small></div></td></tr></tbody></table> <p><b>Divisores</b> são <a href="/wiki/N%C3%BAmeros_inteiros" class="mw-redirect" title="Números inteiros">números inteiros</a> e <a href="/wiki/Racionais" class="mw-redirect mw-disambig" title="Racionais">racionais</a>,<sup id="cite_ref-aurelio_1-0" class="reference"><a href="#cite_note-aurelio-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> sendo o dito divisor y diferente de 0 (y<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }" /></span>0)e o divisor z igualmente (z<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }" /></span>0)<sup id="cite_ref-enio_2-0" class="reference"><a href="#cite_note-enio-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> com os quais se pode efetuar uma divisão de números maiores (igualmente inteiros e racionais), tendo como <a href="/wiki/Resto" class="mw-redirect" title="Resto">resto</a> e <a href="/wiki/Quociente" class="mw-disambig" title="Quociente">quociente</a> uma quantidade exata. </p><p>Exemplo:<sup id="cite_ref-enio_2-1" class="reference"><a href="#cite_note-enio-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,\!{\frac {x}{y}}=z\rightarrow \,\!{\frac {x}{z}}=y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>y</mi> </mfrac> </mrow> <mo>=</mo> <mi>z</mi> <mo stretchy="false">→</mo> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>z</mi> </mfrac> </mrow> <mo>=</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!{\frac {x}{y}}=z\rightarrow \,\!{\frac {x}{z}}=y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbb22872cf789e44e76d7c3dd692fbd624ddfbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.386ex; height:5.176ex;" alt="{\displaystyle \,\!{\frac {x}{y}}=z\rightarrow \,\!{\frac {x}{z}}=y}" /></span> </p><p><br /> Todo e qualquer número tem seus divisores, inclusive os <a href="/wiki/N%C3%BAmeros_primos" class="mw-redirect" title="Números primos">números primos</a>, que só tem como <b>divisores</b> 1 e o dito primo.<sup id="cite_ref-aurelio_1-1" class="reference"><a href="#cite_note-aurelio-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Sobre_os_divisores">Sobre os divisores</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Divisor&veaction=edit&section=1" title="Editar secção: Sobre os divisores" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Divisor&action=edit&section=1" title="Editar código-fonte da secção: Sobre os divisores"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Existem infinitos <a href="/wiki/N%C3%BAmeros_primos" class="mw-redirect" title="Números primos">números primos</a> (ver <a href="/wiki/Teoria_dos_n%C3%BAmeros" title="Teoria dos números">Teoria dos números</a>, seção: Propriedades dos números primos; <a href="/wiki/Teorema_de_Euclides" title="Teorema de Euclides">Teorema de Euclides</a>) e infinitos divisores de números.</li> <li>Para cada número <a href="/wiki/Inteiro" class="mw-redirect" title="Inteiro">inteiro</a> e <a href="/wiki/Racional" class="mw-disambig" title="Racional">racional</a> há um conjunto de divisores que lhe é próprio.</li> <li>Dois números podem ter em comum vários divisores. Quando isto acontece, diz-se que os ditos números fazem parte de mais de um conjunto <a href="/wiki/Matem%C3%A1tico" title="Matemático">matemático</a>.</li></ul> <p>Como exemplo, pode-se citar o número <a href="/wiki/Vinte_e_dois" title="Vinte e dois">22</a>, que pertence ao conjunto de <a href="/wiki/M%C3%BAltiplos" title="Múltiplos">múltiplos</a> de <a href="/wiki/Dois" title="Dois">2</a> e dos <a href="/wiki/M%C3%BAltiplos" title="Múltiplos">múltiplos</a> de <a href="/wiki/Onze" title="Onze">11</a> igualmente, ou seja, os divisores de <a href="/wiki/Vinte_e_dois" title="Vinte e dois">22</a> são <a href="/wiki/Dois" title="Dois">2</a> e <a href="/wiki/Onze" title="Onze">11</a>, além de <a href="/wiki/Um" title="Um">1</a> e <a href="/wiki/Vinte_e_dois" title="Vinte e dois">22</a>. </p><p>No conjunto dos <a href="/wiki/M%C3%BAltiplos" title="Múltiplos">múltiplos</a> de <a href="/wiki/Onze" title="Onze">11</a>:<sup id="cite_ref-enio_2-2" class="reference"><a href="#cite_note-enio-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{11,22,33...\right\}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>{</mo> <mrow> <mn>11</mn> <mo>,</mo> <mn>22</mn> <mo>,</mo> <mn>33...</mn> </mrow> <mo>}</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{11,22,33...\right\}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3efc104eea59d583af50289cd773fbe401df8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:13.695ex; height:2.843ex;" alt="{\displaystyle \left\{11,22,33...\right\}\,\!}" /></span> </p><p>No conjunto dos <a href="/wiki/M%C3%BAltiplos" title="Múltiplos">múltiplos</a> de <a href="/wiki/Dois" title="Dois">2</a>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{2,4,6,8,10,12,14,16,18,20,22,24...\right\}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>{</mo> <mrow> <mn>2</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>12</mn> <mo>,</mo> <mn>14</mn> <mo>,</mo> <mn>16</mn> <mo>,</mo> <mn>18</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>22</mn> <mo>,</mo> <mn>24...</mn> </mrow> <mo>}</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{2,4,6,8,10,12,14,16,18,20,22,24...\right\}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/389f3f79bf27257811b9b5e4e072eb17c40618b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:39.275ex; height:2.843ex;" alt="{\displaystyle \left\{2,4,6,8,10,12,14,16,18,20,22,24...\right\}\,\!}" /></span> </p> <ul><li>Quanto maior o <b>divisor</b>, menor será o resto. É similar a uma <a href="/wiki/Regra_de_tr%C3%AAs" title="Regra de três">regra de três</a> inversamente proporcional, pois, quanto menor o <b>divisor</b> de número qualquer <a href="/wiki/Inteiro" class="mw-redirect" title="Inteiro">inteiro</a> e <a href="/wiki/Racional" class="mw-disambig" title="Racional">racional</a>, maior será o resto.</li> <li>Somente há um número que dividido por qualquer número <a href="/wiki/Inteiro" class="mw-redirect" title="Inteiro">inteiro</a> e <a href="/wiki/Racional" class="mw-disambig" title="Racional">racional</a> tem como resto a mesma quantidade: <a href="/wiki/Zero" class="mw-redirect" title="Zero">0</a>. Quaisquer números divididos ou multiplicados pelo mesmo resultarão em <a href="/wiki/Zero" class="mw-redirect" title="Zero">0</a>;</li></ul> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,\!{\frac {0}{1298}}=0\rightarrow 0.\ 1298=\ 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0</mn> <mn>1298</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo stretchy="false">→</mo> <mn>0.</mn> <mtext> </mtext> <mn>1298</mn> <mo>=</mo> <mtext> </mtext> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!{\frac {0}{1298}}=0\rightarrow 0.\ 1298=\ 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/911bba7e1b842b24b129e1eb96f30fb90b964224" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.242ex; height:5.176ex;" alt="{\displaystyle \,\!{\frac {0}{1298}}=0\rightarrow 0.\ 1298=\ 0}" /></span> </p> <ul><li>Todos os divisores de um número qualquer N podem ser descobertos realizando-se <a href="/wiki/Fatora%C3%A7%C3%A3o" title="Fatoração">Fatoração</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>Nem todos os números maiores possuem muitos divisores. É o caso de muitos números relativamente grandes em quantidade, tais como 158, 302, 218, 514, 614, 866, 914, 1514 e obviamente os <a href="/wiki/N%C3%BAmeros_primos" class="mw-redirect" title="Números primos">números primos</a> (ver também <a href="/wiki/N%C3%BAmero_defectivo" title="Número defectivo">número defectivo</a>). Números relativamente grandes em quantidade que não sejam múltiplos de <a href="/wiki/Tr%C3%AAs" title="Três">3</a>, <a href="/wiki/Quatro" title="Quatro">4</a>, <a href="/wiki/Cinco" title="Cinco">5</a> ou <a href="/wiki/Sete" title="Sete">7</a> tem grandes chances de serem do mesmo caso. Geralmente é um <a href="/wiki/N%C3%BAmero_defectivo" title="Número defectivo">número defectivo</a> ou <a href="/wiki/N%C3%BAmero_deficiente" class="mw-redirect" title="Número deficiente">número deficiente</a> que se encontra nesse caso.</li> <li>Quando determinados números x possuem um determinado divisor N, que multiplicado por N, que possui o mesmo valor de x, diz-se que é um <a href="/wiki/Quadrado_perfeito" class="mw-redirect" title="Quadrado perfeito">quadrado perfeito</a> do número x</li></ul> <p>Exemplo: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5.\ 5=\ 25\rightarrow 5^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5.</mn> <mtext> </mtext> <mn>5</mn> <mo>=</mo> <mtext> </mtext> <mn>25</mn> <mo stretchy="false">→</mo> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5.\ 5=\ 25\rightarrow 5^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/174d30049ade796cbadcd82500c10a397a16c3d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.387ex; height:2.676ex;" alt="{\displaystyle 5.\ 5=\ 25\rightarrow 5^{2}}" /></span> </p><p>Portanto: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,\!{\frac {25}{5}}=5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>25</mn> <mn>5</mn> </mfrac> </mrow> <mo>=</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!{\frac {25}{5}}=5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed51f72abf039c450020ac98f09ab95c222f047b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.422ex; height:5.176ex;" alt="{\displaystyle \,\!{\frac {25}{5}}=5}" /></span> </p> <ul><li>Os números irracionais não podem ser postos em forma de fração (ver também <a href="/wiki/N%C3%BAmeros_irracionais" class="mw-redirect" title="Números irracionais">números irracionais</a>),<sup id="cite_ref-enio_2-3" class="reference"><a href="#cite_note-enio-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> logo não possuem nenhum <b>divisor</b> no <a href="/wiki/N%C3%BAmero_real" title="Número real">conjunto dos números reais</a>. Por exemplo o <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }" /></span>, que é a <a href="/wiki/Propor%C3%A7%C3%A3o" class="mw-redirect" title="Proporção">proporção</a> numérica aproximada (pois é número irracional) oriunda da relação das medidas de <a href="/wiki/Per%C3%ADmetro" title="Perímetro">perímetro</a> de <a href="/wiki/Circunfer%C3%AAncia" title="Circunferência">circunferência</a> e <a href="/wiki/Di%C3%A2metro" title="Diâmetro">diâmetro</a>.</li></ul> <p><br /> </p><p>Sejam <i>n</i>, <i>d</i> e <i>q</i> <a href="/wiki/N%C3%BAmeros_inteiros" class="mw-redirect" title="Números inteiros">números inteiros</a>, com <i>d</i> diferente de zero (d <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }" /></span> 0). Dizemos que <i>d</i> é <b>divisor</b> de <i>n</i> (ou que <i>d</i> divide <i>n</i>, ou ainda que <i>n</i> é divisível por <i>d</i>) se existir um <i>q</i> tal que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q\cdot d=n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo>⋅</mo> <mi>d</mi> <mo>=</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q\cdot d=n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7180a496d6a4322b19a276271606699b9ad7c5d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.458ex; height:2.509ex;" alt="{\displaystyle q\cdot d=n}" /></span> (note que isto é o mesmo que escrever <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bae6bb34bd4f759e0026603bdfaf8714dfce0a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.458ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q}" /></span>) </p><p>Exemplo:<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (n=0)\land (n=d\cdot q)\Rightarrow 0=d\cdot q\Rightarrow q=0,\forall d\in \mathbb {Z} ^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>∧</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇒</mo> <mn>0</mn> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo stretchy="false">⇒</mo> <mi>q</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>d</mi> <mo>∈</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (n=0)\land (n=d\cdot q)\Rightarrow 0=d\cdot q\Rightarrow q=0,\forall d\in \mathbb {Z} ^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/255476f6efcb3da9d34f46b51e4f3fbb57b46408" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:50.086ex; height:2.843ex;" alt="{\displaystyle (n=0)\land (n=d\cdot q)\Rightarrow 0=d\cdot q\Rightarrow q=0,\forall d\in \mathbb {Z} ^{*}}" /></span> <br />(se <i>n</i> é igual a zero, e se ainda <i>n</i> é igual a <i>d</i> vezes <i>q</i>, então zero é igual a <i>d</i> vezes <i>q</i>, de onde se conclui que <i>q</i> deve ser igual a zero, para todo <i>d</i> pertencente a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} ^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} ^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45aa6a166e406bf9e192b7a32d6b140f27cd8538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.605ex; height:2.343ex;" alt="{\displaystyle \mathbb {Z} ^{*}}" /></span>, que é o conjunto dos números inteiros sem o zero) </p><p>Formalmente, se <i>d</i> é divisor de <i>n</i>, então:<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists _{q\in \mathbb {Z} }:n=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∃</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mrow> </msub> <mo>:</mo> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists _{q\in \mathbb {Z} }:n=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d836eaa15c1b081cd9d9979850d3dba157dee3a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.868ex; height:2.843ex;" alt="{\displaystyle \exists _{q\in \mathbb {Z} }:n=d\cdot q}" /></span> <br />(lê-se: <i>existe um número inteiro <b>q</b> tal que <b>n</b> é igual a <b>d</b> vezes <b>q</b></i>) </p><p>Também podemos dizer o seguinte: seja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\in \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\in \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0cdb66fc3217d8a3035bd57ff397ce2d159c0ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.44ex; height:2.176ex;" alt="{\displaystyle r\in \mathbb {Z} }" /></span>. Se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n}{d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>d</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n}{d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08aea70182382a3308aac7a6c9f52ba40389edcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:2.231ex; height:4.843ex;" alt="{\displaystyle {\frac {n}{d}}}" /></span> (<i>n</i> dividido por <i>d</i>) tem <a href="/wiki/Divis%C3%A3o" title="Divisão">quociente</a> <i>q</i> e <a href="/wiki/Resto_da_divis%C3%A3o_inteira" title="Resto da divisão inteira">resto</a> <i>r</i>, então <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f4aa73944bb31455c3d1c6bf269e68dc58aa74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q+r}" /></span> </p><p>Note que há duas situações possíveis para o resto <i>r</i>:<br /> 1) r = 0 <br />Neste caso, dizemos que <i>d</i> <b>divide</b> <i>n</i> (<i>d</i> é divisor de <i>n</i>). Isto porque a expressão <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f4aa73944bb31455c3d1c6bf269e68dc58aa74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q+r}" /></span> será igual à expressão <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q+0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>+</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q+0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25aa3d977509e9084d3936d75dba072635903fe5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.461ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q+0}" /></span>, que é o mesmo que escrever simplesmente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bae6bb34bd4f759e0026603bdfaf8714dfce0a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.458ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q}" /></span>. <br /><i>Nota: como o divisor </i>d<i> não pode ser zero, repare que se </i>n<i> for zero o quociente </i>q<i> também terá que ser zero.</i> <br /><br /> 2) r <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }" /></span> 0 <br />Neste caso, dizemos que <i>d</i> <b>não divide</b> <i>n</i> (<i>d</i> não é divisor de <i>n</i>). Isto porque existe um resto <i>r</i> diferente de zero, ou seja, a expressão <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f4aa73944bb31455c3d1c6bf269e68dc58aa74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q+r}" /></span> <b>não será igual</b> à expressão <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bae6bb34bd4f759e0026603bdfaf8714dfce0a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.458ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q}" /></span>. <br /><i>Nota: podemos escrever <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-r=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>r</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-r=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74511941f0c7a34ce30b2944258b2c18cdc695f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n-r=d\cdot q}" /></span>. O resultado da diferença </i>n-r<i> é um número inteiro. Vamos chamar este número de </i>x<i>, ou seja: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-r=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>r</mi> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-r=x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a43d2ca93f9b3009724aad1ea966cda238c886b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.712ex; height:2.176ex;" alt="{\displaystyle n-r=x}" /></span>. Assim, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d42f6cf629f5bb68f7303a368f37c9b5dd7ddd6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.393ex; height:2.509ex;" alt="{\displaystyle x=d\cdot q}" /></span>. Como </i>d<i> e </i>q<i> também são números inteiros e </i>d<i> é diferente de zero, concluímos que </i>d<i> divide </i>x<i> (</i>d<i> é divisor de </i>x<i>).</i> </p><p>Exemplos: <br />1) A divisão <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {15}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>15</mn> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {15}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36fb95f6811711410edc092f8ce7e33bc9c6ae65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.161ex; height:5.176ex;" alt="{\displaystyle {\frac {15}{3}}}" /></span> tem quociente 5 e resto 0. Assim: <br />O <a href="/wiki/Numerador" class="mw-redirect" title="Numerador">numerador</a> da <a href="/wiki/Fra%C3%A7%C3%A3o" title="Fração">fração</a> é <i>n</i> = 15; <br />O <a href="/wiki/Denominador" class="mw-redirect" title="Denominador">denominador</a> da fração é <i>d</i> = 3; <br />O quociente da <a href="/wiki/Divis%C3%A3o" title="Divisão">divisão</a> é <i>q</i> = 5; <br />O resto da divisão é <i>r</i> = 0. <br /> Como <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f4aa73944bb31455c3d1c6bf269e68dc58aa74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q+r}" /></span>, escrevemos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 15=3\cdot 5+0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>15</mn> <mo>=</mo> <mn>3</mn> <mo>⋅</mo> <mn>5</mn> <mo>+</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 15=3\cdot 5+0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d935264259f9bad1222a21c64657d144f5fbf0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.43ex; height:2.343ex;" alt="{\displaystyle 15=3\cdot 5+0}" /></span>, ou simplesmente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 15=3\cdot 5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>15</mn> <mo>=</mo> <mn>3</mn> <mo>⋅</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 15=3\cdot 5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2248994809a37748a35af3df104b09cc3b979c54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.427ex; height:2.176ex;" alt="{\displaystyle 15=3\cdot 5}" /></span>. <br />Neste exemplo, o denominador <i>d</i> (= 3) <b>divide</b> 15, portanto <i>d</i> também é divisor de 15 (note que <i>r</i> = 0). </p><p><br />2) A divisão <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {7}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {7}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc26ac1e993d93a66fc806702577ea797c2b6865" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {7}{2}}}" /></span> tem quociente 3 e resto 1. Assim: <br />O <a href="/wiki/Numerador" class="mw-redirect" title="Numerador">numerador</a> da <a href="/wiki/Fra%C3%A7%C3%A3o" title="Fração">fração</a> é <i>n</i> = 7; <br />O <a href="/wiki/Denominador" class="mw-redirect" title="Denominador">denominador</a> da fração é <i>d</i> = 2; <br />O quociente da <a href="/wiki/Divis%C3%A3o" title="Divisão">divisão</a> é <i>q</i> = 3; <br />O resto da divisão é <i>r</i> = 1. <br />Como <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=d\cdot q+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=d\cdot q+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f4aa73944bb31455c3d1c6bf269e68dc58aa74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n=d\cdot q+r}" /></span>, escrevemos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 7=2\cdot 3+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>7</mn> <mo>=</mo> <mn>2</mn> <mo>⋅</mo> <mn>3</mn> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 7=2\cdot 3+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05a798ca853b4c3a3297a82c4138d342fc96f55e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.268ex; height:2.343ex;" alt="{\displaystyle 7=2\cdot 3+1}" /></span> <br />Neste exemplo, o denominador <i>d</i> (= 2) <b>não divide</b> 7, portanto <i>d</i> não é divisor de 7 (note que <i>r</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }" /></span> 0). <br />Porém, lembre-se de que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-r=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>r</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-r=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74511941f0c7a34ce30b2944258b2c18cdc695f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n-r=d\cdot q}" /></span>. Isto significa que <i>d</i> divide <i>n - r</i> (<i>d</i> é divisor de <i>n - r</i>). Conferindo: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28d2048804ba61b4fc8761e42223f561e0a7ce6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.477ex; height:2.176ex;" alt="{\displaystyle d=2}" /></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-r=7-1=6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>r</mi> <mo>=</mo> <mn>7</mn> <mo>−</mo> <mn>1</mn> <mo>=</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-r=7-1=6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8284aea45efa1a80bed1d8328185121582dbbe34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.808ex; height:2.343ex;" alt="{\displaystyle n-r=7-1=6}" /></span>. Como <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\cdot q=2\cdot 3=6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> <mo>=</mo> <mn>2</mn> <mo>⋅</mo> <mn>3</mn> <mo>=</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\cdot q=2\cdot 3=6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c9a23f09427d34ace666e4b051656a9c9587758" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.328ex; height:2.509ex;" alt="{\displaystyle d\cdot q=2\cdot 3=6}" /></span>, ambas as expressões <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86c0aa8d9c52b096540edd6e6a91eb8f790a8b7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.284ex; height:2.176ex;" alt="{\displaystyle n-r}" /></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84519945211e38585e6920d7fc695d4909da7be6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.965ex; height:2.509ex;" alt="{\displaystyle d\cdot q}" /></span> valem 6, portanto elas são iguais, e por isto podemos escrever <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-r=d\cdot q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mi>r</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-r=d\cdot q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74511941f0c7a34ce30b2944258b2c18cdc695f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.347ex; height:2.509ex;" alt="{\displaystyle n-r=d\cdot q}" /></span>. Logo, <i>d</i> divide <i>n - r</i>, ou seja, 2 divide 6 (2 é divisor de 6). </p> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. 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