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<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_ur.wikipedia.org&uselang=ur" class=""><span>عطیہ دیجیے</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=%D8%AE%D8%A7%D8%B5:%D8%AA%D8%AE%D9%84%DB%8C%D9%82_%DA%A9%DA%BE%D8%A7%D8%AA%DB%81&returnto=%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81" title="کھاتہ بنانے یا اس میں داخل ہونے کی سفارش کی جاتی ہے؛ تاہم یہ ضروری نہیں" class=""><span>کھاتہ بنائیں</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=%D8%AE%D8%A7%D8%B5:%D8%AF%D8%A7%D8%AE%D9%84_%DB%81%D9%88%DA%BA&returnto=%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81" title="کھاتے میں داخل ہونے کی سفارش کی جاتی ہے؛ تاہم یہ ضروری نہیں [o]" accesskey="o" class=""><span>داخل ہوں</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="مزید اختیارات" > <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="ذاتی آلات" > <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">ذاتی آلات</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" 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_ur.wikipedia.org&uselang=ur"><span>عطیہ دیجیے</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:%D8%AA%D8%AE%D9%84%DB%8C%D9%82_%DA%A9%DA%BE%D8%A7%D8%AA%DB%81&returnto=%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81" title="کھاتہ بنانے یا اس میں داخل ہونے کی سفارش کی جاتی ہے؛ تاہم یہ ضروری نہیں"><span class="vector-icon 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href="/wiki/%D8%AE%D8%A7%D8%B5:%D9%85%DB%8C%D8%B1%DB%8C_%D8%B4%D8%B1%D8%A7%DA%A9%D8%AA%DB%8C%DA%BA" title="اس آئی پی پتے سے انجام دی جانے والی تمام ترامیم کی فہرست [y]" accesskey="y"><span>شراکتیں</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:%D9%85%DB%8C%D8%B1%D8%A7_%D8%AA%D8%A8%D8%A7%D8%AF%D9%84%DB%81_%D8%AE%DB%8C%D8%A7%D9%84" title="اس آئی پی پتے کی ترامیم سے متعلق گفتگو [n]" accesskey="n"><span>تبادلۂ خیال</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="ویب گاہ"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="مندرجات" 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">مندرجات</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">بغلی پٹی پر جائیں</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">چھپائیں</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">دیباچہ</div> </a> </li> <li id="toc-تعریف" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#تعریف"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>تعریف</span> </div> </a> <ul id="toc-تعریف-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-مزید_دیکھیے" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#مزید_دیکھیے"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>مزید دیکھیے</span> </div> </a> <ul id="toc-مزید_دیکھیے-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-حوالہ_جات" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#حوالہ_جات"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>حوالہ جات</span> </div> </a> <ul id="toc-حوالہ_جات-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="مندرجات" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="فہرست عناوین دیکھیں" > <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">فہرست عناوین دیکھیں</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">عاملیہ</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="Go to an article in another language. Available in 80 languages" > <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 زبانیں</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <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 – عربی" lang="ar" hreflang="ar" data-title="عاملي" data-language-autonym="العربية" data-language-local-name="عربی" class="interlanguage-link-target"><span>العربية</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 – فارسی" lang="fa" hreflang="fa" data-title="فاکتوریل" data-language-autonym="فارسی" data-language-local-name="فارسی" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="بہترین مضمون"><a href="https://en.wikipedia.org/wiki/Factorial" title="Factorial – انگریزی" lang="en" hreflang="en" data-title="Factorial" data-language-autonym="English" data-language-local-name="انگریزی" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Fakulteit_(wiskunde)" title="Fakulteit (wiskunde) – افریقی" lang="af" hreflang="af" data-title="Fakulteit (wiskunde)" data-language-autonym="Afrikaans" data-language-local-name="افریقی" 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 – امہاری" lang="am" hreflang="am" data-title="ፋክቶሪያል" data-language-autonym="አማርኛ" data-language-local-name="امہاری" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Factorial" title="Factorial – اسٹوریائی" lang="ast" hreflang="ast" data-title="Factorial" data-language-autonym="Asturianu" data-language-local-name="اسٹوریائی" 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 – آذربائیجانی" lang="az" hreflang="az" data-title="Faktorial" data-language-autonym="Azərbaycanca" data-language-local-name="آذربائیجانی" class="interlanguage-link-target"><span>Azərbaycanca</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 – بنگلہ" lang="bn" hreflang="bn" data-title="গৌণিক" data-language-autonym="বাংলা" data-language-local-name="بنگلہ" class="interlanguage-link-target"><span>বাংলা</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 – باشکیر" lang="ba" hreflang="ba" data-title="Факториал" data-language-autonym="Башҡортса" data-language-local-name="باشکیر" 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 – بیلاروسی" lang="be" hreflang="be" data-title="Фактарыял" data-language-autonym="Беларуская" data-language-local-name="بیلاروسی" 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 – بلغاری" lang="bg" hreflang="bg" data-title="Факториел" data-language-autonym="Български" data-language-local-name="بلغاری" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Faktorijel" title="Faktorijel – بوسنیائی" lang="bs" hreflang="bs" data-title="Faktorijel" data-language-autonym="Bosanski" data-language-local-name="بوسنیائی" 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 – کیٹالان" lang="ca" hreflang="ca" data-title="Factorial" data-language-autonym="Català" data-language-local-name="کیٹالان" class="interlanguage-link-target"><span>Català</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 – چوواش" lang="cv" hreflang="cv" data-title="Факториал" data-language-autonym="Чӑвашла" data-language-local-name="چوواش" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Faktori%C3%A1l" title="Faktoriál – چیک" lang="cs" hreflang="cs" data-title="Faktoriál" data-language-autonym="Čeština" data-language-local-name="چیک" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Fakultet_(matematik)" title="Fakultet (matematik) – ڈینش" lang="da" hreflang="da" data-title="Fakultet (matematik)" data-language-autonym="Dansk" data-language-local-name="ڈینش" 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) – جرمن" lang="de" hreflang="de" data-title="Fakultät (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="جرمن" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Faktoriaal" title="Faktoriaal – اسٹونین" lang="et" hreflang="et" data-title="Faktoriaal" data-language-autonym="Eesti" data-language-local-name="اسٹونین" class="interlanguage-link-target"><span>Eesti</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 – یونانی" lang="el" hreflang="el" data-title="Παραγοντικό" data-language-autonym="Ελληνικά" data-language-local-name="یونانی" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Factorial" title="Factorial – ہسپانوی" lang="es" hreflang="es" data-title="Factorial" data-language-autonym="Español" data-language-local-name="ہسپانوی" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Faktorialo" title="Faktorialo – ایسپرانٹو" lang="eo" hreflang="eo" data-title="Faktorialo" data-language-autonym="Esperanto" data-language-local-name="ایسپرانٹو" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Faktorial" title="Faktorial – باسکی" lang="eu" hreflang="eu" data-title="Faktorial" data-language-autonym="Euskara" data-language-local-name="باسکی" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Factorielle" title="Factorielle – فرانسیسی" lang="fr" hreflang="fr" data-title="Factorielle" data-language-autonym="Français" data-language-local-name="فرانسیسی" 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 – گالیشیائی" lang="gl" hreflang="gl" data-title="Factorial" data-language-autonym="Galego" data-language-local-name="گالیشیائی" class="interlanguage-link-target"><span>Galego</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) – کوریائی" lang="ko" hreflang="ko" data-title="계승 (수학)" data-language-autonym="한국어" data-language-local-name="کوریائی" class="interlanguage-link-target"><span>한국어</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 – آرمینیائی" lang="hy" hreflang="hy" data-title="Ֆակտորիալ" data-language-autonym="Հայերեն" data-language-local-name="آرمینیائی" class="interlanguage-link-target"><span>Հայերեն</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 – ہندی" lang="hi" hreflang="hi" data-title="क्रमगुणित" data-language-autonym="हिन्दी" data-language-local-name="ہندی" 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 – کراتی" lang="hr" hreflang="hr" data-title="Faktorijel" data-language-autonym="Hrvatski" data-language-local-name="کراتی" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Faktorialo" title="Faktorialo – ایڈو" lang="io" hreflang="io" data-title="Faktorialo" data-language-autonym="Ido" data-language-local-name="ایڈو" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Faktorial" title="Faktorial – انڈونیثیائی" lang="id" hreflang="id" data-title="Faktorial" data-language-autonym="Bahasa Indonesia" data-language-local-name="انڈونیثیائی" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Factorial" title="Factorial – بین لسانیات" lang="ia" hreflang="ia" data-title="Factorial" data-language-autonym="Interlingua" data-language-local-name="بین لسانیات" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/A%C3%B0feldi" title="Aðfeldi – آئس لینڈک" lang="is" hreflang="is" data-title="Aðfeldi" data-language-autonym="Íslenska" data-language-local-name="آئس لینڈک" 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 – اطالوی" lang="it" hreflang="it" data-title="Fattoriale" data-language-autonym="Italiano" data-language-local-name="اطالوی" class="interlanguage-link-target"><span>Italiano</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) – عبرانی" lang="he" hreflang="he" data-title="עצרת (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="عبرانی" class="interlanguage-link-target"><span>עברית</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 – کنّاڈا" lang="kn" hreflang="kn" data-title="ಕ್ರಮಗುಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="کنّاڈا" class="interlanguage-link-target"><span>ಕನ್ನಡ</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 – جارجیائی" lang="ka" hreflang="ka" data-title="მათემატიკური ფაქტორიალი" data-language-autonym="ქართული" data-language-local-name="جارجیائی" 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 – قزاخ" lang="kk" hreflang="kk" data-title="Факториал" data-language-autonym="Қазақша" data-language-local-name="قزاخ" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Factorialis" title="Factorialis – لاطینی" lang="la" hreflang="la" data-title="Factorialis" data-language-autonym="Latina" data-language-local-name="لاطینی" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Faktori%C4%81ls" title="Faktoriāls – لیٹوین" lang="lv" hreflang="lv" data-title="Faktoriāls" data-language-autonym="Latviešu" data-language-local-name="لیٹوین" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Faktorialas" title="Faktorialas – لیتھوینین" lang="lt" hreflang="lt" data-title="Faktorialas" data-language-autonym="Lietuvių" data-language-local-name="لیتھوینین" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fatorial" title="Fatorial – لومبارڈ" lang="lmo" hreflang="lmo" data-title="Fatorial" data-language-autonym="Lombard" data-language-local-name="لومبارڈ" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Faktori%C3%A1lis" title="Faktoriális – ہنگیرین" lang="hu" hreflang="hu" data-title="Faktoriális" data-language-autonym="Magyar" data-language-local-name="ہنگیرین" class="interlanguage-link-target"><span>Magyar</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 – مقدونیائی" lang="mk" hreflang="mk" data-title="Факториел" data-language-autonym="Македонски" data-language-local-name="مقدونیائی" 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 – مالایالم" lang="ml" hreflang="ml" data-title="ക്രമഗുണിതം" data-language-autonym="മലയാളം" data-language-local-name="مالایالم" 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 – مراٹهی" lang="mr" hreflang="mr" data-title="क्रमगुणित" data-language-autonym="मराठी" data-language-local-name="مراٹهی" 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 – مالے" lang="ms" hreflang="ms" data-title="Faktorial" data-language-autonym="Bahasa Melayu" data-language-local-name="مالے" 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) – ڈچ" lang="nl" hreflang="nl" data-title="Faculteit (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="ڈچ" class="interlanguage-link-target"><span>Nederlands</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 – جاپانی" lang="ja" hreflang="ja" data-title="階乗" data-language-autonym="日本語" data-language-local-name="جاپانی" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Fakultet_(matematikk)" title="Fakultet (matematikk) – نارویجین بوکمل" lang="nb" hreflang="nb" data-title="Fakultet (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="نارویجین بوکمل" class="interlanguage-link-target"><span>Norsk bokmål</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 – نارویجین نینورسک" lang="nn" hreflang="nn" data-title="Fakultet i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="نارویجین نینورسک" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Factoriala" title="Factoriala – آکسیٹان" lang="oc" hreflang="oc" data-title="Factoriala" data-language-autonym="Occitan" data-language-local-name="آکسیٹان" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Faktorial" title="Faktorial – ازبیک" lang="uz" hreflang="uz" data-title="Faktorial" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ازبیک" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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 – پنجابی" lang="pa" hreflang="pa" data-title="ਕ੍ਰਮਗੁਣਿਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="پنجابی" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Silnia" title="Silnia – پولش" lang="pl" hreflang="pl" data-title="Silnia" data-language-autonym="Polski" data-language-local-name="پولش" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fatorial" title="Fatorial – پُرتگالی" lang="pt" hreflang="pt" data-title="Fatorial" data-language-autonym="Português" data-language-local-name="پُرتگالی" 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 – رومینین" lang="ro" hreflang="ro" data-title="Factorial" data-language-autonym="Română" data-language-local-name="رومینین" 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 – روسی" lang="ru" hreflang="ru" data-title="Факториал" data-language-autonym="Русский" data-language-local-name="روسی" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Faktoriali" title="Faktoriali – البانی" lang="sq" hreflang="sq" data-title="Faktoriali" data-language-autonym="Shqip" data-language-local-name="البانی" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Fatturiali" title="Fatturiali – سیسیلین" lang="scn" hreflang="scn" data-title="Fatturiali" data-language-autonym="Sicilianu" data-language-local-name="سیسیلین" class="interlanguage-link-target"><span>Sicilianu</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 – سنہالا" lang="si" hreflang="si" data-title="ක්‍රමාරෝපිතය" data-language-autonym="සිංහල" data-language-local-name="سنہالا" 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 – سلوواک" lang="sk" hreflang="sk" data-title="Faktoriál" data-language-autonym="Slovenčina" data-language-local-name="سلوواک" 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) – سلووینیائی" lang="sl" hreflang="sl" data-title="Fakulteta (funkcija)" data-language-autonym="Slovenščina" data-language-local-name="سلووینیائی" class="interlanguage-link-target"><span>Slovenščina</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 – سینٹرل کردش" lang="ckb" hreflang="ckb" data-title="فاکتۆریێل" data-language-autonym="کوردی" data-language-local-name="سینٹرل کردش" class="interlanguage-link-target"><span>کوردی</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 – سربین" lang="sr" hreflang="sr" data-title="Факторијел" data-language-autonym="Српски / srpski" data-language-local-name="سربین" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Faktorijel" title="Faktorijel – سربو-کروئیشین" lang="sh" hreflang="sh" data-title="Faktorijel" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="سربو-کروئیشین" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kertoma" title="Kertoma – فینیش" lang="fi" hreflang="fi" data-title="Kertoma" data-language-autonym="Suomi" data-language-local-name="فینیش" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Fakultet_(matematik)" title="Fakultet (matematik) – سویڈش" lang="sv" hreflang="sv" data-title="Fakultet (matematik)" data-language-autonym="Svenska" data-language-local-name="سویڈش" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Paktoryal" title="Paktoryal – ٹیگا لوگ" lang="tl" hreflang="tl" data-title="Paktoryal" data-language-autonym="Tagalog" data-language-local-name="ٹیگا لوگ" class="interlanguage-link-target"><span>Tagalog</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 – تمل" lang="ta" hreflang="ta" data-title="தொடர் பெருக்கம்" data-language-autonym="தமிழ்" data-language-local-name="تمل" 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 – تھائی" lang="th" hreflang="th" data-title="แฟกทอเรียล" data-language-autonym="ไทย" data-language-local-name="تھائی" 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 – ترکی" lang="tr" hreflang="tr" data-title="Faktöriyel" data-language-autonym="Türkçe" data-language-local-name="ترکی" 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 – یوکرینیائی" lang="uk" hreflang="uk" data-title="Факторіал" data-language-autonym="Українська" data-language-local-name="یوکرینیائی" class="interlanguage-link-target"><span>Українська</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 – ویتنامی" lang="vi" hreflang="vi" data-title="Giai thừa" data-language-autonym="Tiếng Việt" data-language-local-name="ویتنامی" class="interlanguage-link-target"><span>Tiếng Việt</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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%98%B6%E4%B9%98" title="阶乘 – وو چائینیز" lang="wuu" hreflang="wuu" data-title="阶乘" data-language-autonym="吴语" data-language-local-name="وو چائینیز" class="interlanguage-link-target"><span>吴语</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 – کینٹونیز" lang="yue" hreflang="yue" data-title="階乘" data-language-autonym="粵語" data-language-local-name="کینٹونیز" class="interlanguage-link-target"><span>粵語</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 – چینی" lang="zh" hreflang="zh" data-title="階乘" data-language-autonym="中文" data-language-local-name="چینی" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Faktorial" title="Faktorial – ایبان" lang="iba" hreflang="iba" data-title="Faktorial" data-language-autonym="Jaku Iban" data-language-local-name="ایبان" class="interlanguage-link-target"><span>Jaku Iban</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="ترمیم بین اللسانی روابط" class="wbc-editpage">ترمیم روابط</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="فضائے نام"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs 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class="mw-body-content"><div class="mw-content-rtl mw-parser-output" lang="ur" dir="rtl"><table class="mw-collapsible mw-expanded wikitable" style="float:left; clear:left; margin:0 1em 0.4em 0em;"> <tbody><tr> <th>اصطلاح </th> <th>term </th></tr> <tr> <td> <p>عامِلیہ <sup id="cite_ref-1" class="reference" style="font-size: 75%;"><a href="#cite_note-1">[1]</a></sup> </p> </td> <td style="text-align:left; font-family:arial; direction:LTR;"> <p>Factorial </p> </td></tr></tbody></table> <div class="thumb tleft"><div style="width:20em;" dir="ltr"> <table class="wikitable" style="width:100%; margin:0;" cellspacing="0"> <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"> <mtext> </mtext> <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/04d5ee46b14bb2dc4043b06e1f7a7141eb08e065" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.622ex; 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>5040 </td></tr> <tr> <td>8</td> <td>40320 </td></tr> <tr> <td>9</td> <td>362880 </td></tr> <tr> <td>10</td> <td>3628800 </td></tr> <tr> <td>15</td> <td>1307674368000 </td></tr> <tr> <td>20</td> <td>2432902008176640000 </td></tr> <tr> <td>25</td> <td>15511210043330985984000000 </td></tr> <tr> <td>50</td> <td>3.04140932... × 10<sup>64</sup> </td></tr> <tr> <td>70</td> <td>1.19785717... × 10<sup>100</sup> </td></tr> <tr> <td>450</td> <td>1.73336873... × 10<sup>1,000</sup> </td></tr> <tr> <td>3249</td> <td>6.41233768... × 10<sup>10,000</sup> </td></tr> <tr> <td>25206</td> <td>1.205703438... × 10<sup>100,000</sup> </td></tr> <tr> <td>100000</td> <td>2.8242294079... × 10<sup>456,573</sup> </td></tr></tbody></table> </div></div> <p>کسی غیر منفی <a href="/wiki/%D8%B5%D8%AD%DB%8C%D8%AD_%D8%B9%D8%AF%D8%AF" title="صحیح عدد">صحیح عدد</a> <i>n</i> کا عاملیہ اس عدد سے چھوٹے مثبت صحیح اعداد کا حاصل ضرب تعریف کیا جاتا ہے۔ عدد <i>n</i> کا عاملیہ <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"> <mtext> </mtext> <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/04d5ee46b14bb2dc4043b06e1f7a7141eb08e065" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.622ex; height:2.176ex;" alt="{\displaystyle \ n!}"></span> لکھا جاتا ہے۔ مثلاً </p> <dl><dd><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!=1\times 2\times 3\times 4\times 5=120\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>!</mo> <mo>=</mo> <mn>1</mn> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>3</mn> <mo>×</mo> <mn>4</mn> <mo>×</mo> <mn>5</mn> <mo>=</mo> <mn>120</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5!=1\times 2\times 3\times 4\times 5=120\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc5ec1d2511cda61891b758bd11d4756bcb8d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:29.248ex; height:2.176ex;" alt="{\displaystyle 5!=1\times 2\times 3\times 4\times 5=120\ }"></span></dd></dl> <p>جدول میں دیکھو کہ عاملیہ کی قدر بہت تیزی سے بڑھتی ہے جب <i>n</i> بڑا ہو۔ </p> <div class="mw-heading mw-heading2"><h2 id="تعریف"><span id=".D8.AA.D8.B9.D8.B1.DB.8C.D9.81"></span>تعریف</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81&action=edit&section=1" title="تدوینِ قطعہ: تعریف"><span>ترمیم</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>عاملیہ فنکشن یوں تعریف ہوتا ہے </p> <dl><dd><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!=\prod _{k=1}^{n}k\qquad \forall n\in \mathbb {N} .\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>!</mo> <mo>=</mo> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mi>k</mi> <mspace width="2em" /> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>.</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n!=\prod _{k=1}^{n}k\qquad \forall n\in \mathbb {N} .\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e853505f1e8b4acb7bbc73d1e1190c7281d2a2ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.204ex; width:22.022ex; height:6.843ex;" alt="{\displaystyle n!=\prod _{k=1}^{n}k\qquad \forall n\in \mathbb {N} .\!}"></span></dd></dl> <p>غور کرو کہ </p> <dl><dd><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 0!=1\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>!</mo> <mo>=</mo> <mn>1</mn> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0!=1\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dcb339c1ab8f1019944d88381b4f0e1801e427e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.651ex; height:2.176ex;" alt="{\displaystyle 0!=1\ }"></span></dd></dl> <p>یعنی صفر کا عاملیہ ایک ہوتا ہے۔ یہ مفید ہے کیونکہ <a href="/wiki/%D8%B1%D9%8E%D8%AC%D8%B9%D8%AA_%D9%86%D8%B3%D8%A8%D8%AA" class="mw-redirect" title="رَجعت نسبت">رَجعت نسبت</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+1)!=n!\times (n+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> <mo>=</mo> <mi>n</mi> <mo>!</mo> <mo>×</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (n+1)!=n!\times (n+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c768ba65d7631768f8d90872d0069d8ea0dc412" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.041ex; height:2.843ex;" alt="{\displaystyle (n+1)!=n!\times (n+1)}"></span> کام کرتی ہے <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26819344e55f5e671c76c07c18eb4291fcec85ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=0}"></span> کے لیے۔ </p> <div class="mw-heading mw-heading2"><h2 id="مزید_دیکھیے"><span id=".D9.85.D8.B2.DB.8C.D8.AF_.D8.AF.DB.8C.DA.A9.DA.BE.DB.8C.DB.92"></span>مزید دیکھیے</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81&action=edit&section=2" title="تدوینِ قطعہ: مزید دیکھیے"><span>ترمیم</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D8%B3%D9%B9%D8%B1%D9%84%D9%86%DA%AF_%DA%A9%D9%84%DB%8C%DB%81" title="سٹرلنگ کلیہ">سٹرلنگ کلیہ</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="حوالہ_جات"><span id=".D8.AD.D9.88.D8.A7.D9.84.DB.81_.D8.AC.D8.A7.D8.AA"></span>حوالہ جات</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%B9%D8%A7%D9%85%D9%84%DB%8C%DB%81&action=edit&section=3" title="تدوینِ قطعہ: حوالہ جات"><span>ترمیم</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r4721619">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">م پر زیر اور ی پر تشدید کے ساتھ ادا کیا جاتا ہے</span> </li> </ol></div></div> <div style="background-color: #f9f9f9; border: 1px dashed #aaaaaa; padding: .2em; text-align: center; margin: .5em 5em .5em 5em; font-size: large;"><small> </small><p><small><code>E=mc<sup>2</sup></code>     اردو ویکیپیڈیا پر ریاضی مساوات کو بائیں سے دائیں <small>LTR</small> پڑھیٔے     <a href="https://en.wikipedia.org/wiki/Table_of_mathematical_symbols" class="extiw" title="en:Table of mathematical symbols">ریاضی علامات </a></small> </p> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">اخذ کردہ از «<a dir="ltr" href="https://ur.wikipedia.org/w/index.php?title=عاملیہ&oldid=4545746">https://ur.wikipedia.org/w/index.php?title=عاملیہ&oldid=4545746</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D9%85%D8%B9%D8%A7%D9%88%D9%86%D8%AA:%D8%B2%D9%85%D8%B1%DB%81" class="mw-redirect" title="معاونت:زمرہ">زمرہ جات</a>: <ul><li><a href="/wiki/%D8%B2%D9%85%D8%B1%DB%81:%D8%AA%D8%B1%DA%A9%DB%8C%D8%A8%DB%8C%D8%A7%D8%AA" title="زمرہ:ترکیبیات">ترکیبیات</a></li><li><a href="/wiki/%D8%B2%D9%85%D8%B1%DB%81:%D9%86%D8%B8%D8%B1%DB%8C%DB%82_%D8%B9%D8%AF%D8%AF" title="زمرہ:نظریۂ عدد">نظریۂ عدد</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">پوشیدہ زمرہ جات: <ul><li><a href="/wiki/%D8%B2%D9%85%D8%B1%DB%81:%DA%A9%D8%A7%D9%85%D9%86%D8%B2_%D8%B2%D9%85%D8%B1%DB%81_%D8%AC%D8%B3_%DA%A9%D8%A7_%D8%B1%D8%A8%D8%B7_%D9%88%DB%8C%DA%A9%DB%8C_%DA%88%DB%8C%D9%B9%D8%A7_%D9%BE%D8%B1_%DB%81%DB%92" title="زمرہ:کامنز زمرہ جس کا ربط ویکی ڈیٹا پر ہے">کامنز زمرہ جس کا ربط ویکی ڈیٹا پر ہے</a></li><li><a href="/wiki/%D8%B2%D9%85%D8%B1%DB%81:%DA%86%DA%BE%D9%88%D9%B9%DB%92_%D9%BE%DB%8C%D8%BA%D8%A7%D9%85_%D8%AE%D8%A7%D9%86%D9%88%DA%BA_%DA%A9%D8%A7_%D8%A7%D8%B3%D8%AA%D8%B9%D9%85%D8%A7%D9%84_%DA%A9%D8%B1%D9%86%DB%92_%D9%88%D8%A7%D9%84%DB%92_%D9%85%D8%B6%D8%A7%D9%85%DB%8C%D9%86" title="زمرہ:چھوٹے پیغام خانوں کا استعمال کرنے والے مضامین">چھوٹے پیغام خانوں کا استعمال کرنے والے مضامین</a></li></ul></div></div> </div> </main> </div> <div 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