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type="application/atom+xml" title="Atom feed ng Wikipedia" href="/w/index.php?title=Natatangi:Mga_huling_binago&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Paktoryal rootpage-Paktoryal skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Pumunta sa nilalaman</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Sayt"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Pangunahing pagpipilian" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Pangunahing pagpipilian</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Pangunahing pagpipilian</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">itago</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Maglibot </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Unang_Pahina" title="Puntahan ang unang pahina [z]" accesskey="z"><span>Unang pahina</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Tingnan_ang_buod" title="Mga gabay sa pagbabasa ng laktaw-laktaw sa Wikipedia"><span>Mga nilalaman</span></a></li><li id="n-Napiling-nilalaman" class="mw-list-item"><a href="/wiki/Wikipedia:Mga_napiling_artikulo"><span>Napiling nilalaman</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Natatangi:Alin_man" title="Magpalabas ng kahit-anong artikulo [x]" accesskey="x"><span>Alinmang artikulo</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:Patungkol"><span>Patungkol sa Wikipedia</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Wikipedia:Kasalukuyang_pangyayari" title="Hanapin ang mga impormasyon tungkol sa mga kamakailang kaganapan"><span>Mga kaganapan</span></a></li> </ul> </div> </div> <div id="p-Pakikihalubilo" class="vector-menu mw-portlet mw-portlet-Pakikihalubilo" > <div class="vector-menu-heading"> Pakikihalubilo </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Puntahan_ng_pamayanan" title="Tungkol sa proyekto, ano ang maari mong gawin, at kung saan maari maghanap ng mga bagay"><span>Pamayanan</span></a></li><li id="n-Kapihan" class="mw-list-item"><a href="/wiki/Wikipedia:Kapihan"><span>Kapihan</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Natatangi:Mga_huling_binago" title="Tala ng mga huling pagbabago sa wiki. [r]" accesskey="r"><span>Mga huling binago</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Wikipedia:Makipag-ugnayan_sa_amin" title="Paano makokontak ang Wikipedia"><span>Makipag-ugnayan</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Wikipedia:Tulong" title="Ang lugar para maghanap ng tulong sa Wikipedia."><span>Tulong</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Unang_Pahina" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Ang Malayang Ensiklopedya" src="/static/images/mobile/copyright/wikipedia-tagline-tl.svg" width="119" height="13" style="width: 7.4375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Natatangi:Maghanap" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Maghanap sa Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Hanapin</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Maghanap sa Wikipedia" aria-label="Maghanap sa Wikipedia" autocapitalize="sentences" title="Maghanap sa Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Natatangi:Maghanap"> </div> <button class="cdx-button cdx-search-input__end-button">Hanapin</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Mga pansariling kagamitan"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itsura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itsura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itsura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tl.wikipedia.org&uselang=tl" class=""><span>Donasyon</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Natatangi:Likhain_ang_kuwenta&returnto=Paktoryal" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito" class=""><span>Gumawa ng account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Natatangi:Paglagda_ng_tagagamit&returnto=Paktoryal" title="Mas maganda kung magla-login ka; gayunpaman, hindi ka pinipilit gawin ito [o]" accesskey="o" class=""><span>Mag-login</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Marami pang pagpipilian" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Mga pansariling kagamitan" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Mga pansariling kagamitan</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tl.wikipedia.org&uselang=tl"><span>Donasyon</span></a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/Natatangi:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Mag-ambag</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Natatangi:Likhain_ang_kuwenta&returnto=Paktoryal" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Gumawa ng account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Natatangi:Paglagda_ng_tagagamit&returnto=Paktoryal" title="Mas maganda kung magla-login ka; gayunpaman, hindi ka pinipilit gawin ito [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Mag-login</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Mga pahina para sa naka-logout na mga patnugot o editor <a href="/wiki/Wikipedia:Maligayang_pagdating!" aria-label="Alamin pa ang tungkol sa pagpapatnugot"><span>alamin pa</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Natatangi:Usapan_ko" title="Usapang tungkol sa mga pagbabagong ginawa sa ip address na ito [n]" accesskey="n"><span>Usapan</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sayt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Paktoryal</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="Pumunta sa isang artikulo na nakasulat sa ibang wika. Mayroon ito sa 80 (na) wika" > <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-80" 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">80 wika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Fakulteit_(wiskunde)" title="Fakulteit (wiskunde) – Afrikaans" lang="af" hreflang="af" data-title="Fakulteit (wiskunde)" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8D%8B%E1%8A%AD%E1%89%B6%E1%88%AA%E1%8B%AB%E1%88%8D" title="ፋክቶሪያል – Amharic" lang="am" hreflang="am" data-title="ፋክቶሪያል" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%A7%D9%85%D9%84%D9%8A" title="عاملي – Arabic" lang="ar" hreflang="ar" data-title="عاملي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Factorial" title="Factorial – Asturian" lang="ast" hreflang="ast" data-title="Factorial" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Faktorial" title="Faktorial – Azerbaijani" lang="az" hreflang="az" data-title="Faktorial" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB" title="Факториал – Bashkir" lang="ba" hreflang="ba" data-title="Факториал" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%B0%D1%80%D1%8B%D1%8F%D0%BB" title="Фактарыял – Belarusian" lang="be" hreflang="be" data-title="Фактарыял" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B5%D0%BB" title="Факториел – Bulgarian" lang="bg" hreflang="bg" data-title="Факториел" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A7%8C%E0%A6%A3%E0%A6%BF%E0%A6%95" title="গৌণিক – Bangla" lang="bn" hreflang="bn" data-title="গৌণিক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Faktorijel" title="Faktorijel – Bosnian" lang="bs" hreflang="bs" data-title="Faktorijel" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Factorial" title="Factorial – Catalan" lang="ca" hreflang="ca" data-title="Factorial" data-language-autonym="Català" data-language-local-name="Catalan" 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/%D9%81%D8%A7%DA%A9%D8%AA%DB%86%D8%B1%DB%8C%DB%8E%D9%84" title="فاکتۆریێل – Central Kurdish" lang="ckb" hreflang="ckb" data-title="فاکتۆریێل" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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/Faktori%C3%A1l" title="Faktoriál – Czech" lang="cs" hreflang="cs" data-title="Faktoriál" data-language-autonym="Čeština" data-language-local-name="Czech" 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%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB" title="Факториал – Chuvash" lang="cv" hreflang="cv" data-title="Факториал" 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/Fakultet_(matematik)" title="Fakultet (matematik) – Danish" lang="da" hreflang="da" data-title="Fakultet (matematik)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fakult%C3%A4t_(Mathematik)" title="Fakultät (Mathematik) – German" lang="de" hreflang="de" data-title="Fakultät (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%B1%CF%81%CE%B1%CE%B3%CE%BF%CE%BD%CF%84%CE%B9%CE%BA%CF%8C" title="Παραγοντικό – Greek" lang="el" hreflang="el" data-title="Παραγοντικό" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://en.wikipedia.org/wiki/Factorial" title="Factorial – English" lang="en" hreflang="en" data-title="Factorial" data-language-autonym="English" data-language-local-name="English" 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/Faktorialo" title="Faktorialo – Esperanto" lang="eo" hreflang="eo" data-title="Faktorialo" 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/Factorial" title="Factorial – Spanish" lang="es" hreflang="es" data-title="Factorial" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Faktoriaal" title="Faktoriaal – Estonian" lang="et" hreflang="et" data-title="Faktoriaal" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Faktorial" title="Faktorial – Basque" lang="eu" hreflang="eu" data-title="Faktorial" data-language-autonym="Euskara" data-language-local-name="Basque" 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%81%D8%A7%DA%A9%D8%AA%D9%88%D8%B1%DB%8C%D9%84" title="فاکتوریل – Persian" lang="fa" hreflang="fa" data-title="فاکتوریل" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Kertoma" title="Kertoma – Finnish" lang="fi" hreflang="fi" data-title="Kertoma" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Factorielle" title="Factorielle – French" lang="fr" hreflang="fr" data-title="Factorielle" data-language-autonym="Français" data-language-local-name="French" 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/Factorial" title="Factorial – Galician" lang="gl" hreflang="gl" data-title="Factorial" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%A6%D7%A8%D7%AA_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="עצרת (מתמטיקה) – Hebrew" lang="he" hreflang="he" data-title="עצרת (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="Hebrew" 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%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="क्रमगुणित – Hindi" lang="hi" hreflang="hi" data-title="क्रमगुणित" 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/Faktorijel" title="Faktorijel – Croatian" lang="hr" hreflang="hr" data-title="Faktorijel" data-language-autonym="Hrvatski" data-language-local-name="Croatian" 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/Faktori%C3%A1lis" title="Faktoriális – Hungarian" lang="hu" hreflang="hu" data-title="Faktoriális" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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/%D5%96%D5%A1%D5%AF%D5%BF%D5%B8%D6%80%D5%AB%D5%A1%D5%AC" title="Ֆակտորիալ – Armenian" lang="hy" hreflang="hy" data-title="Ֆակտորիալ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Factorial" title="Factorial – Interlingua" lang="ia" hreflang="ia" data-title="Factorial" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Faktorial" title="Faktorial – Iban" lang="iba" hreflang="iba" data-title="Faktorial" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Faktorial" title="Faktorial – Indonesian" lang="id" hreflang="id" data-title="Faktorial" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" 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/Faktorialo" title="Faktorialo – Ido" lang="io" hreflang="io" data-title="Faktorialo" 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/A%C3%B0feldi" title="Aðfeldi – Icelandic" lang="is" hreflang="is" data-title="Aðfeldi" data-language-autonym="Íslenska" data-language-local-name="Icelandic" 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/Fattoriale" title="Fattoriale – Italian" lang="it" hreflang="it" data-title="Fattoriale" data-language-autonym="Italiano" data-language-local-name="Italian" 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/%E9%9A%8E%E4%B9%97" title="階乗 – Japanese" lang="ja" hreflang="ja" data-title="階乗" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A4%E1%83%90%E1%83%A5%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90%E1%83%9A%E1%83%98" title="მათემატიკური ფაქტორიალი – Georgian" lang="ka" hreflang="ka" data-title="მათემატიკური ფაქტორიალი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB" title="Факториал – Kazakh" lang="kk" hreflang="kk" data-title="Факториал" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B3%8D%E0%B2%B0%E0%B2%AE%E0%B2%97%E0%B3%81%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಕ್ರಮಗುಣಿತ – Kannada" lang="kn" hreflang="kn" data-title="ಕ್ರಮಗುಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%84%EC%8A%B9_(%EC%88%98%ED%95%99)" title="계승 (수학) – Korean" lang="ko" hreflang="ko" data-title="계승 (수학)" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Factorialis" title="Factorialis – Latin" lang="la" hreflang="la" data-title="Factorialis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fatorial" title="Fatorial – Lombard" lang="lmo" hreflang="lmo" data-title="Fatorial" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Faktorialas" title="Faktorialas – Lithuanian" lang="lt" hreflang="lt" data-title="Faktorialas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Faktori%C4%81ls" title="Faktoriāls – Latvian" lang="lv" hreflang="lv" data-title="Faktoriāls" data-language-autonym="Latviešu" data-language-local-name="Latvian" 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%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B5%D0%BB" title="Факториел – Macedonian" lang="mk" hreflang="mk" data-title="Факториел" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%8D%E0%B4%B0%E0%B4%AE%E0%B4%97%E0%B5%81%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ക്രമഗുണിതം – Malayalam" lang="ml" hreflang="ml" data-title="ക്രമഗുണിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="क्रमगुणित – Marathi" lang="mr" hreflang="mr" data-title="क्रमगुणित" data-language-autonym="मराठी" data-language-local-name="Marathi" 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/Faktorial" title="Faktorial – Malay" lang="ms" hreflang="ms" data-title="Faktorial" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Faculteit_(wiskunde)" title="Faculteit (wiskunde) – Dutch" lang="nl" hreflang="nl" data-title="Faculteit (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/Fakultet_i_matematikk" title="Fakultet i matematikk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Fakultet i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Fakultet_(matematikk)" title="Fakultet (matematikk) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Fakultet (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Factoriala" title="Factoriala – Occitan" lang="oc" hreflang="oc" data-title="Factoriala" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%8D%E0%A8%B0%E0%A8%AE%E0%A8%97%E0%A9%81%E0%A8%A3%E0%A8%BF%E0%A8%A4" title="ਕ੍ਰਮਗੁਣਿਤ – Punjabi" lang="pa" hreflang="pa" data-title="ਕ੍ਰਮਗੁਣਿਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Silnia" title="Silnia – Polish" lang="pl" hreflang="pl" data-title="Silnia" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Fatorial" title="Fatorial – Piedmontese" lang="pms" hreflang="pms" data-title="Fatorial" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fatorial" title="Fatorial – Portuguese" lang="pt" hreflang="pt" data-title="Fatorial" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Factorial" title="Factorial – Romanian" lang="ro" hreflang="ro" data-title="Factorial" data-language-autonym="Română" data-language-local-name="Romanian" 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%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB" title="Факториал – Russian" lang="ru" hreflang="ru" data-title="Факториал" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Fatturiali" title="Fatturiali – Sicilian" lang="scn" hreflang="scn" data-title="Fatturiali" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Faktorijel" title="Faktorijel – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Faktorijel" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B7%8F%E0%B6%BB%E0%B7%9D%E0%B6%B4%E0%B7%92%E0%B6%AD%E0%B6%BA" title="ක්‍රමාරෝපිතය – Sinhala" lang="si" hreflang="si" data-title="ක්‍රමාරෝපිතය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Factorial" title="Factorial – Simple English" lang="en-simple" hreflang="en-simple" data-title="Factorial" 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/Faktori%C3%A1l" title="Faktoriál – Slovak" lang="sk" hreflang="sk" data-title="Faktoriál" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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/Fakulteta_(funkcija)" title="Fakulteta (funkcija) – Slovenian" lang="sl" hreflang="sl" data-title="Fakulteta (funkcija)" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Faktoriali" title="Faktoriali – Albanian" lang="sq" hreflang="sq" data-title="Faktoriali" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%98%D0%B5%D0%BB" title="Факторијел – Serbian" lang="sr" hreflang="sr" data-title="Факторијел" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Fakultet_(matematik)" title="Fakultet (matematik) – Swedish" lang="sv" hreflang="sv" data-title="Fakultet (matematik)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%9F%E0%AE%B0%E0%AF%8D_%E0%AE%AA%E0%AF%86%E0%AE%B0%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%AE%E0%AF%8D" title="தொடர் பெருக்கம் – Tamil" lang="ta" hreflang="ta" data-title="தொடர் பெருக்கம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%9F%E0%B8%81%E0%B8%97%E0%B8%AD%E0%B9%80%E0%B8%A3%E0%B8%B5%E0%B8%A2%E0%B8%A5" title="แฟกทอเรียล – Thai" lang="th" hreflang="th" data-title="แฟกทอเรียล" data-language-autonym="ไทย" data-language-local-name="Thai" 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/Fakt%C3%B6riyel" title="Faktöriyel – Turkish" lang="tr" hreflang="tr" data-title="Faktöriyel" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D1%96%D0%B0%D0%BB" title="Факторіал – Ukrainian" lang="uk" hreflang="uk" data-title="Факторіал" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81" title="عاملیہ – Urdu" lang="ur" hreflang="ur" data-title="عاملیہ" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Faktorial" title="Faktorial – Uzbek" lang="uz" hreflang="uz" data-title="Faktorial" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" 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/Giai_th%E1%BB%ABa" title="Giai thừa – Vietnamese" lang="vi" hreflang="vi" data-title="Giai thừa" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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/%E9%98%B6%E4%B9%98" title="阶乘 – Wu" lang="wuu" hreflang="wuu" data-title="阶乘" 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/%E9%9A%8E%E4%B9%98" title="階乘 – Chinese" lang="zh" hreflang="zh" data-title="階乘" data-language-autonym="中文" data-language-local-name="Chinese" 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/%E9%9A%8E%E4%B9%98" title="階乘 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="階乘" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9A%8E%E4%B9%98" title="階乘 – Cantonese" lang="yue" hreflang="yue" data-title="階乘" data-language-autonym="粵語" data-language-local-name="Cantonese" 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/Q120976#sitelinks-wikipedia" title="Baguhin ang link sa ibang wika" class="wbc-editpage">baguhin ang mga link</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="Namespace"> <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/Paktoryal" title="Tingnan ang nilalaman [c]" accesskey="c"><span>Artikulo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Usapan:Paktoryal&action=edit&redlink=1" rel="discussion" class="new" title="Usapan tungkol sa nilalaman nito (hindi pa naisusulat) [t]" accesskey="t"><span>Usapan</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="Ibahin ang baryante o variant ng wika" > <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">Tagalog</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="Mga tingin"> <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/Paktoryal"><span>Basahin</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Paktoryal&veaction=edit" title="Baguhin ito [v]" accesskey="v"><span>Baguhin</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Paktoryal&action=edit" title="Baguhin ang kodigong batayan ng pahinang ito [e]" accesskey="e"><span>Baguhin ang wikitext</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Paktoryal&action=history" title="Nakaraang pagbabago sa pahinang ito [h]" accesskey="h"><span>Tingnan ang kasaysayan</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <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="Mga kagamitan" > <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">Mga kagamitan</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">Mga kagamitan</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">itago</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Mga aksyon </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/Paktoryal"><span>Basahin</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Paktoryal&veaction=edit" title="Baguhin ito [v]" accesskey="v"><span>Baguhin</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Paktoryal&action=edit" title="Baguhin ang kodigong batayan ng pahinang ito [e]" accesskey="e"><span>Baguhin ang wikitext</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Paktoryal&action=history"><span>Tingnan ang kasaysayan</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Pangkalahatan </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Natatangi:Ano_ang_nakakawing_dito/Paktoryal" title="Talaan ng mga pahinang wiking nakaturo rito. [j]" accesskey="j"><span>Mga nakaturo rito</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Natatangi:Nakakawing_ng_kamakailang_pagbabago/Paktoryal" rel="nofollow" title="Mga huling binago sa mga kaugnay na pahina mula sa pahinang ito [k]" accesskey="k"><span>Kaugnay na pagbabago</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=tl" title="Magkarga ng mga larawan o iba pang midya [u]" accesskey="u"><span>Mag-upload ng file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Natatangi:Natatanging_mga_pahina" title="Tala ng mga natatanging pahina [q]" accesskey="q"><span>Natatanging pahina</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Paktoryal&oldid=2020716" title="Ibigay ang palagiang kawing para sa kasalukuyang bersyon ng pahinang ito"><span>Permanenteng link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Paktoryal&action=info" title="More information about this page"><span>Impormasyon ng pahina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Natatangi:Sipiin&page=Paktoryal&id=2020716&wpFormIdentifier=titleform" title="Impormasyon sa pagsangguni sa pahinang ito"><span>Sumangguni</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Natatangi:UrlShortener&url=https%3A%2F%2Ftl.wikipedia.org%2Fwiki%2FPaktoryal"><span>Kumuha ng pinaikling URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Natatangi:QrCode&url=https%3A%2F%2Ftl.wikipedia.org%2Fwiki%2FPaktoryal"><span>I-download ang QR code</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"> I-print/I-export </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=Natatangi:Aklat&bookcmd=book_creator&referer=Paktoryal"><span>Lumikha ng isang aklat</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Natatangi:DownloadAsPdf&page=Paktoryal&action=show-download-screen"><span>I-download bilang PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Paktoryal&printable=yes" title="Ipakita ang bersyon ng pahinang itong madaling maililimbag [p]" accesskey="p"><span>Bersyong mapi-print</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Sa iba pang proyekto </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Factorial_(function)" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikifunctions mw-list-item"><a href="https://www.wikifunctions.org/wiki/Z13667" hreflang="en"><span>Wikifunctions</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q120976" title="Link sa nakakonektang item sa repositoryo ng datos [g]" accesskey="g"><span>Item na Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Itsura"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Itsura</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">itago</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">Mula sa Wikipedia, ang malayang ensiklopedya</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="tl" dir="ltr"><div role="note" class="hatnote navigation-not-searchable">Huwag ikalito sa <a href="/wiki/Paktorya" class="mw-redirect" title="Paktorya">Paktorya</a>.</div> <table class="wikitable" style="margin:0 0 0 1em; text-align:right; float:right;"> <caption>Mga paktorial na nakapipili; pinapantay ang mga saysay sa <a href="/w/index.php?title=Notasyong_pang-agham&action=edit&redlink=1" class="new" title="Notasyong pang-agham (hindi pa naisusulat)">notasyong pang-agham</a> </caption> <tbody><tr> <th><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> </th> <th><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!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>!</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bae971720be3cc9b8d82f4cdac89cb89877514a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.042ex; height:2.176ex;" alt="{\displaystyle n!}"></span> </th></tr> <tr> <td>0</td> <td>1 </td></tr> <tr> <td>1</td> <td>1 </td></tr> <tr> <td>2</td> <td>2 </td></tr> <tr> <td>3</td> <td>6 </td></tr> <tr> <td>4</td> <td>24 </td></tr> <tr> <td>5</td> <td>120 </td></tr> <tr> <td>6</td> <td>720 </td></tr> <tr> <td>7</td> <td><span class="nowrap"><span data-sort-value="7003504000000000000♠"></span>5<span style="margin-left:.25em;">040</span></span> </td></tr> <tr> <td>8</td> <td><span class="nowrap"><span data-sort-value="7004403200000000000♠"></span>40<span style="margin-left:.25em;">320</span></span> </td></tr> <tr> <td>9</td> <td><span class="nowrap"><span data-sort-value="7005362880000000000♠"></span>362<span style="margin-left:.25em;">880</span></span> </td></tr> <tr> <td>10</td> <td><span class="nowrap"><span data-sort-value="7006362880000000000♠"></span>3<span style="margin-left:.25em;">628</span><span style="margin-left:.25em;">800</span></span> </td></tr> <tr> <td>11</td> <td><span class="nowrap"><span data-sort-value="7007399168000000000♠"></span>39<span style="margin-left:.25em;">916</span><span style="margin-left:.25em;">800</span></span> </td></tr> <tr> <td>12</td> <td><span class="nowrap"><span data-sort-value="7008479001600000000♠"></span>479<span style="margin-left:.25em;">001</span><span style="margin-left:.25em;">600</span></span> </td></tr> <tr> <td>13</td> <td><span class="nowrap"><span data-sort-value="7009622702080000000♠"></span>6<span style="margin-left:.25em;">227</span><span style="margin-left:.25em;">020</span><span style="margin-left:.25em;">800</span></span> </td></tr> <tr> <td>14</td> <td><span class="nowrap"><span data-sort-value="7010871782912000000♠"></span>87<span style="margin-left:.25em;">178</span><span style="margin-left:.25em;">291</span><span style="margin-left:.25em;">200</span></span> </td></tr> <tr> <td>15</td> <td><span class="nowrap"><span data-sort-value="7012130767436800000♠"></span>1<span style="margin-left:.25em;">307</span><span style="margin-left:.25em;">674</span><span style="margin-left:.25em;">368</span><span style="margin-left:.25em;">000</span></span> </td></tr> <tr> <td>16</td> <td><span class="nowrap"><span data-sort-value="7013209227898880000♠"></span>20<span style="margin-left:.25em;">922</span><span style="margin-left:.25em;">789</span><span style="margin-left:.25em;">888</span><span style="margin-left:.25em;">000</span></span> </td></tr> <tr> <td>17</td> <td><span class="nowrap"><span data-sort-value="7014355687428096000♠"></span>355<span style="margin-left:.25em;">687</span><span style="margin-left:.25em;">428</span><span style="margin-left:.25em;">096</span><span style="margin-left:.25em;">000</span></span> </td></tr> <tr> <td>18</td> <td><span class="nowrap"><span data-sort-value="7015640237370572800♠"></span>6<span style="margin-left:.25em;">402</span><span style="margin-left:.25em;">373</span><span style="margin-left:.25em;">705</span><span style="margin-left:.25em;">728</span><span style="margin-left:.25em;">000</span></span> </td></tr> <tr> <td>19</td> <td><span class="nowrap"><span data-sort-value="7017121645100408832♠"></span>121<span style="margin-left:.25em;">645</span><span style="margin-left:.25em;">100</span><span style="margin-left:.25em;">408</span><span style="margin-left:.25em;">832</span><span style="margin-left:.25em;">000</span></span> </td></tr> <tr> <td>20</td> <td><span class="nowrap"><span data-sort-value="7018243290200817664♠"></span>2<span style="margin-left:.25em;">432</span><span style="margin-left:.25em;">902</span><span style="margin-left:.25em;">008</span><span style="margin-left:.25em;">176</span><span style="margin-left:.25em;">640</span><span style="margin-left:.25em;">000</span></span> </td></tr> <tr> <td>25 </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="7025155112100400000♠"></span>1.551<span style="margin-left:.25em;">121</span><span style="margin-left:.25em;">004</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>25</sup></span> </td></tr> <tr> <td>50 </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="7064304140932000000♠"></span>3.041<span style="margin-left:.25em;">409</span><span style="margin-left:.25em;">320</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>64</sup></span> </td></tr> <tr> <td>70 </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="7100119785716700000♠"></span>1.197<span style="margin-left:.25em;">857</span><span style="margin-left:.25em;">167</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>100</sup></span> </td></tr> <tr> <td>100 </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="7157933262154400000♠"></span>9.332<span style="margin-left:.25em;">621</span><span style="margin-left:.25em;">544</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>157</sup></span> </td></tr> <tr> <td>450 </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>1.733<span style="margin-left:.25em;">368</span><span style="margin-left:.25em;">733</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>1<span style="margin-left:.25em;">000</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1<span style="margin-left:.25em;">000</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>4.023<span style="margin-left:.25em;">872</span><span style="margin-left:.25em;">601</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2<span style="margin-left:.25em;">567</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7003324900000000000♠"></span>3<span style="margin-left:.25em;">249</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>6.412<span style="margin-left:.25em;">337</span><span style="margin-left:.25em;">688</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>10<span style="margin-left:.25em;">000</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7004100000000000000♠"></span>10<span style="margin-left:.25em;">000</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>2.846<span style="margin-left:.25em;">259</span><span style="margin-left:.25em;">681</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>35<span style="margin-left:.25em;">659</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7004252060000000000♠"></span>25<span style="margin-left:.25em;">206</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>1.205<span style="margin-left:.25em;">703</span><span style="margin-left:.25em;">438</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>100<span style="margin-left:.25em;">000</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7005100000000000000♠"></span>100<span style="margin-left:.25em;">000</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>2.824<span style="margin-left:.25em;">229</span><span style="margin-left:.25em;">408</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>456<span style="margin-left:.25em;">573</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7005205023000000000♠"></span>205<span style="margin-left:.25em;">023</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>2.503<span style="margin-left:.25em;">898</span><span style="margin-left:.25em;">932</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>1<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">004</span></sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7006100000000000000♠"></span>1<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span></span> </td> <td style="text-align:left"><span class="nowrap"><span data-sort-value="9000000000000000000♠"></span>8.263<span style="margin-left:.25em;">931</span><span style="margin-left:.25em;">688</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>5<span style="margin-left:.25em;">565</span><span style="margin-left:.25em;">708</span></sup></span> </td></tr> <tr> <td><a href="/wiki/Googol" title="Googol"><span class="nowrap"><span data-sort-value="7100100000000000000♠"></span>10<sup>100</sup></span></a></td> <td>10<sup><span class="nowrap"><span data-sort-value="7101995657055180894♠"></span>10<sup>101.998<span style="margin-left:.25em;">109</span><span style="margin-left:.25em;">775</span><span style="margin-left:.25em;">4820</span></sup></span></sup> </td></tr></tbody></table> <p>Sa <a href="/wiki/Matematika" title="Matematika">matematika</a>, lalo na sa <a href="/wiki/Kombinatorika" title="Kombinatorika">kombinatorika</a>, ang <b>paktoryal</b> (<a href="/wiki/Ingles" class="mw-redirect" title="Ingles">Ingles</a> at <a href="/wiki/Wikang_Kastila" title="Wikang Kastila">Kastila</a>: <i>factorial</i>) ng isang di-negatibong <a href="/wiki/Buumbilang" title="Buumbilang">buumbilang</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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>, itinala ng <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!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>!</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bae971720be3cc9b8d82f4cdac89cb89877514a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.042ex; height:2.176ex;" alt="{\displaystyle n!}"></span>, ay <a href="/wiki/Pagpaparami_(matematika)" title="Pagpaparami (matematika)">pagpaparami</a> ng lahat ng mga positibong buumbilang menos kaysa o katumbas sa <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>. Ang paktoryal ng <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> din ay katumbas sa bunga ng <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> at kasunod na mas maliit na paktoryal: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}n!&=n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 3\times 2\times 1\\&=n\times (n-1)!\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>n</mi> <mo>!</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>n</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mo>⋯</mo> <mo>×</mo> <mn>3</mn> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>n</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}n!&=n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 3\times 2\times 1\\&=n\times (n-1)!\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb20c62aa91c3705daae002fc76b8df34db4d494" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:55ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}n!&=n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 3\times 2\times 1\\&=n\times (n-1)!\\\end{aligned}}}"></span> </p><p>Halimbawa, </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5!=5\times 4!=5\times 4\times 3\times 2\times 1=120.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>!</mo> <mo>=</mo> <mn>5</mn> <mo>×</mo> <mn>4</mn> <mo>!</mo> <mo>=</mo> <mn>5</mn> <mo>×</mo> <mn>4</mn> <mo>×</mo> <mn>3</mn> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> <mo>=</mo> <mn>120.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5!=5\times 4!=5\times 4\times 3\times 2\times 1=120.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3411d81e0c8b9cf8aa4e8220a2d67e77840b9031" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:38.225ex; height:2.176ex;" alt="{\displaystyle 5!=5\times 4!=5\times 4\times 3\times 2\times 1=120.}"></span> </p><p>Ang saysay ng 0! ay 1, ayon sa kumbensyon para sa isang basyong bunga (<a href="/wiki/Wikang_Ingles" title="Wikang Ingles">Ingles</a>: <i lang="en">empty product</i>). </p><p>Nadiskubre ang mga paktoryal ng maraming sinaunang kultura, lalo na sa matematikang <a href="/wiki/Indiya" title="Indiya">Indiyano</a> sa kanonikong mga obra ng panitikan ng <a href="/wiki/Hainismo" title="Hainismo">Hainismo</a>, at ng mga mistikong Hudyo sa Talmudikong aklat <i>Sefer Yetzirah</i>. Hinahanap ang <a href="/wiki/Operasyon_(matematika)" title="Operasyon (matematika)">operasyong</a> paktoryal sa maraming <a href="/w/index.php?title=Sangay_ng_matematika&action=edit&redlink=1" class="new" title="Sangay ng matematika (hindi pa naisusulat)">sangay ng matematika</a>, lalo na sa <a href="/wiki/Kombinatorika" title="Kombinatorika">kombinatorika</a>, kung saan ang pinakabasal na paggamit ay bumibilang ng mga posibleng natatanging <a href="/w/index.php?title=Sekwensiya&action=edit&redlink=1" class="new" title="Sekwensiya (hindi pa naisusulat)">sekwensiya</a> — mga <a href="/wiki/Permutasyon" title="Permutasyon">permutasyon</a> — ng <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> natatanging bagay: may <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!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>!</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bae971720be3cc9b8d82f4cdac89cb89877514a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.042ex; height:2.176ex;" alt="{\displaystyle n!}"></span>. Sa <a href="/wiki/Pagsusuring_matematikal" title="Pagsusuring matematikal">pagsusuring matematikal</a>, ginagamit ang mga paktoryal sa mga <a href="/wiki/Makapangyarihang_serye" title="Makapangyarihang serye">makapangyarihang serye</a> para sa <a href="/wiki/Eksponensiyal_na_punsiyon" title="Eksponensiyal na punsiyon">eksponensiyal na punsiyon</a> at ibang mga <a href="/wiki/Punsiyon_(matematika)" title="Punsiyon (matematika)">punsiyon</a>, at saka may mga aplikasyon sa <a href="/wiki/Alhebra" title="Alhebra">alhebra</a>, <a href="/wiki/Teorya_ng_bilang" title="Teorya ng bilang">teorya ng bilang</a>, <a href="/wiki/Teorya_ng_probabilidad" title="Teorya ng probabilidad">teorya ng probabilidad</a>, at <a href="/wiki/Agham_pangkompyuter" title="Agham pangkompyuter">agham pangkompyuter</a>. </p><p>Nilinang ang karamihan ng matematika ng punsiyong paktoryal noong huling bahagi ng ika-18 at unang bahagi ng ika-19 na mga siglo. Idinudulot ng <a href="/w/index.php?title=Aproksimasyon_ni_Stirling&action=edit&redlink=1" class="new" title="Aproksimasyon ni Stirling (hindi pa naisusulat)">aproksimasyon ni Stirling</a> ang tamang aproksimasyon ng mga paktoryal ng mga malalaking bilang, at ipinapakita na lumalaki mas mabilis kaysa sa <a href="/w/index.php?title=Eksponensiyal_na_paglaki&action=edit&redlink=1" class="new" title="Eksponensiyal na paglaki (hindi pa naisusulat)">eksponensiyal na paglaki</a>. Inilalarawan ng <a href="/w/index.php?title=Pormula_ni_Legendre&action=edit&redlink=1" class="new" title="Pormula ni Legendre (hindi pa naisusulat)">pormula ni Legendre</a> ang mga <a href="/wiki/Eksponente" title="Eksponente">eksponente</a> ng mga <a href="/wiki/Pangunahing_bilang" title="Pangunahing bilang">pangunahing bilang</a> sa <a href="/w/index.php?title=Pangunahing_paktorisasyon&action=edit&redlink=1" class="new" title="Pangunahing paktorisasyon (hindi pa naisusulat)">pangunahing paktorisasyon</a> ng mga paktoryal, at nagagamit para sa bumilang ng pinal na mga <a href="/wiki/Sero" class="mw-redirect" title="Sero">sero</a> ng mga paktoryal. Nagamit nina <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a> at <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> ang paktoryal na punsiyon sa <a href="/w/index.php?title=Patuloy_na_punsiyon&action=edit&redlink=1" class="new" title="Patuloy na punsiyon (hindi pa naisusulat)">patuloy na punsiyon</a> ng mga <a href="/wiki/Komplikadong_bilang" title="Komplikadong bilang">komplikadong bilang</a>, kundi sa mga negatibong mga buumbilang, sa madaling salita, ang <a href="/w/index.php?title=Punsiyong_gama&action=edit&redlink=1" class="new" title="Punsiyong gama (hindi pa naisusulat)">punsiyong gama</a> (<a href="/wiki/Wikang_Ingles" title="Wikang Ingles">Ingles</a>: <i lang="en">gamma function</i>, o <span class="texhtml">Γ</span>). </p><p>Ang maraming ibang sikat na mga punsiyon at mga sekwensiya ng bilang ay malapit na kaugnay sa mga paktoryal. Mga ito ay sumasaklaw ng <a href="/w/index.php?title=Koepisyenteng_binomyal&action=edit&redlink=1" class="new" title="Koepisyenteng binomyal (hindi pa naisusulat)">koepisyenteng binomyal</a>, ng <a href="/w/index.php?title=Dobleng_paktoryal&action=edit&redlink=1" class="new" title="Dobleng paktoryal (hindi pa naisusulat)">dobleng paktoryal</a>, ng <a href="/w/index.php?title=Paktoryal_na_nagbabawas&action=edit&redlink=1" class="new" title="Paktoryal na nagbabawas (hindi pa naisusulat)">paktoryal na nagbabawas</a>, ng <a href="/w/index.php?title=Primoryal&action=edit&redlink=1" class="new" title="Primoryal (hindi pa naisusulat)">primoryal</a>, at ng <a href="/w/index.php?title=Subpaktoryal&action=edit&redlink=1" class="new" title="Subpaktoryal (hindi pa naisusulat)">subpaktoryal</a>. Ang mga implementasyon ng paktoryal na punsiyon ay karaniwan na ginagamit para sa ipakita ang mga estilo sa <a href="/wiki/Pagpoprograma_sa_kompyuter" title="Pagpoprograma sa kompyuter">pagpoprograma sa kompyuter</a>, at sinasaklaw sa mga <a href="/w/index.php?title=Kalkulador_pang-agham&action=edit&redlink=1" class="new" title="Kalkulador pang-agham (hindi pa naisusulat)">kalkulador pang-agham</a>. </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Kinuha sa "<a dir="ltr" href="https://tl.wikipedia.org/w/index.php?title=Paktoryal&oldid=2020716">https://tl.wikipedia.org/w/index.php?title=Paktoryal&oldid=2020716</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Natatangi:Mga_kategorya" title="Natatangi:Mga kategorya">Kategorya</a>: <ul><li><a href="/wiki/Kategorya:Kombinatorika" title="Kategorya:Kombinatorika">Kombinatorika</a></li><li><a href="/wiki/Kategorya:Elementaryong_Alhebra" title="Kategorya:Elementaryong Alhebra">Elementaryong Alhebra</a></li><li><a href="/wiki/Kategorya:Mga_punsiyon_at_pagmamapa" title="Kategorya:Mga punsiyon at pagmamapa">Mga punsiyon at pagmamapa</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Nakatagong kategorya: <ul><li><a href="/wiki/Kategorya:Mga_artikulong_naglalaman_ng_Ingles" title="Kategorya:Mga artikulong naglalaman ng Ingles">Mga artikulong naglalaman ng Ingles</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Huling pagbabago: 19:34, 19 Mayo 2023.</li> <li id="footer-info-copyright">Magagamit ang teksto sa ilalim ng <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Lisensyang Creative Commons Attribution/Share-Alike</a>; maaaring mailapat ang karagdagang termino. 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