{"id":3764,"date":"2024-06-05T09:20:45","date_gmt":"2024-06-05T09:20:45","guid":{"rendered":"https:\/\/calculator6.com\/?p=3764"},"modified":"2025-03-13T14:40:02","modified_gmt":"2025-03-13T14:40:02","slug":"faktoriyel-hesaplama","status":"publish","type":"post","link":"https:\/\/www.calculator6.com\/tr\/faktoriyel-hesaplama\/","title":{"rendered":"Fakt\u00f6riyel Hesaplama"},"content":{"rendered":"<p>Fakt\u00f6riyel hesaplay\u0131c\u0131, belirli bir say\u0131n\u0131n fakt\u00f6riyelini h\u0131zl\u0131 ve do\u011fru bir \u015fekilde hesaplaman\u0131za olanak tan\u0131yan bir ara\u00e7t\u0131r. Fakt\u00f6riyel kavram\u0131 matematikte yayg\u0131n olarak kullan\u0131lmaktad\u0131r ve \u00f6zellikle kombinatorik ve olas\u0131l\u0131k teorisi gibi alanlarda \u00f6nemlidir. Fakt\u00f6riyel hesaplay\u0131c\u0131, fakt\u00f6riyel i\u015flemi matematiksel olarak h\u0131zl\u0131 ve do\u011fru bir \u015fekilde ger\u00e7ekle\u015ftirmenizi sa\u011flar. \u00d6zellikle b\u00fcy\u00fck say\u0131larla \u00e7al\u0131\u015f\u0131rken hata yapma riskini ortadan kald\u0131rarak i\u015flemlerinizi kolayla\u015ft\u0131r\u0131r.<\/p>\n<p>Online fakt\u00f6riyel hesap makinesini kullan\u0131rken: Say\u0131 bilgilerini girerek hesaplama yapabilirsiniz.<\/p>\n<hr \/>\n<div id=\"434\"><div class=\"formbox-wrapper\"><form action=\"https:\/\/www.calculator6.com\/tr\/faktoriyel-hesaplama\/\" name=\"formbox\" class=\"formbox formbox-434\" id=\"calculator_434\" data-trp-original-action=\"https:\/\/www.calculator6.com\/tr\/faktoriyel-hesaplama\/\">\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<fieldset class=\"formbox__container\"><div class=\"formbox__title\">Say\u0131<\/div><div class=\"formbox__body\"><div class=\"formbox__field\" style=\"box-shadow: none\"><label class=\"formbox__field-lable\" for=\"formbox-field-1\">Say\u0131<\/label><input type=\"number\" class=\"formbox__field-input\" value=\"\" required=\"\" name=\"formbox-field-1\" id=\"formbox-field-1\"><\/div><\/div> <\/fieldset><fieldset class=\"formbox__container\"><div class=\"formbox__title\"><\/div><div class=\"formbox__body\"><div class=\"formbox__field\"><label class=\"formbox__field-lable\" for=\"formbox-field-2\"><\/label><select class=\"formbox__field-select\" name=\"formbox-field-2\" id=\"formbox-field-2\"><option value=\"1\">fakt\u00f6rden say\u0131ya<\/option><option value=\"2\">say\u0131dan fakt\u00f6re<\/option><\/select><\/div><\/div> <\/fieldset><fieldset class=\"formbox__container\"><div class=\"formbox__title\"><\/div><div class=\"formbox__body\"><div class=\"formbox__btn\"><button class=\"formbox__btn-calc\">Hesapla<\/button><button type=\"reset\" class=\"formbox__btn-reset\">S\u0131f\u0131rla<\/button><\/div><\/div> <\/fieldset><fieldset class=\"formbox__container has-result is-hidden\"><div class=\"formbox__title\">Sonu\u00e7<\/div><div class=\"formbox__body\"><div class=\"formbox__field is-result\" style=\"box-shadow: none\"><label class=\"formbox__field-lable\" for=\"formbox-field-3\">Sonu\u00e7<\/label><input type=\"text\" class=\"formbox__field-result\" readonly=\"\" name=\"formbox-field-3\" id=\"formbox-field-3\"><\/div><\/div> <\/fieldset>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<fieldset class=\"formbox__container formbox__wpcf7 has-result is-hidden\"><div class=\"formbox__title\"><\/div><div class=\"formbox__body\"><div class=\"formbox__btn\"><span class=\"formbox__btn-mail\" tabindex=\"0\">E-posta ile Payla\u015f<\/span><\/div><\/div> <\/fieldset><input type=\"hidden\" class=\"calc-not-change\"><input type=\"hidden\" name=\"trp-form-language\" value=\"tr\"\/><\/form><div class=\"formbox__popup\">\r\n\t\t\t            <div class=\"formbox__popup-wrapper\">\r\n\t\t\t                <div class=\"formbox__popup-header\">\r\n\t\t\t                    <div class=\"formbox__popup-title\">E-posta ile Payla\u015f<\/div>\r\n\t\t\t                    <button class=\"formbox__popup-close\"><\/button>\r\n\t\t\t                <\/div>\r\n\t\t\t                <div class=\"formbox__popup-content\">\r\n\t\t\t                    \r\n\t\t\t                <\/div>\r\n\t\t\t                <div class=\"formbox__popup-form\">\r\n\t\t\t                    \n<div class=\"wpcf7 no-js\" id=\"wpcf7-f1349-o1\" lang=\"tr-TR\" dir=\"ltr\" data-wpcf7-id=\"1349\">\n<div class=\"screen-reader-response\"><p role=\"status\" aria-live=\"polite\" aria-atomic=\"true\"><\/p> <ul><\/ul><\/div>\n<form action=\"\/tr\/wp-json\/wp\/v2\/posts\/3764#wpcf7-f1349-o1\" method=\"post\" class=\"wpcf7-form init\" aria-label=\"\u0130leti\u015fim Formu\" novalidate=\"novalidate\" data-status=\"init\" data-trp-original-action=\"\/tr\/wp-json\/wp\/v2\/posts\/3764#wpcf7-f1349-o1\">\n<div style=\"display: none;\">\n<input type=\"hidden\" name=\"_wpcf7\" value=\"1349\" \/>\n<input type=\"hidden\" name=\"_wpcf7_version\" value=\"6.0.6\" \/>\n<input type=\"hidden\" name=\"_wpcf7_locale\" value=\"tr_TR\" \/>\n<input type=\"hidden\" name=\"_wpcf7_unit_tag\" value=\"wpcf7-f1349-o1\" \/>\n<input type=\"hidden\" name=\"_wpcf7_container_post\" value=\"0\" \/>\n<input type=\"hidden\" name=\"_wpcf7_posted_data_hash\" value=\"\" \/>\n<\/div>\n<div class=\"field has-addons mx-5\">\n\t<div class=\"control\">\n\t\t<p><span class=\"wpcf7-form-control-wrap\" data-name=\"your-email\"><input size=\"40\" maxlength=\"400\" class=\"wpcf7-form-control wpcf7-email wpcf7-validates-as-required wpcf7-text wpcf7-validates-as-email input\" autocomplete=\"email\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"E-posta adresinizi girin\" value=\"\" type=\"email\" name=\"your-email\" \/><\/span>\n\t\t<\/p>\n\t<\/div>\n\t<div class=\"control\">\n\t\t<p><input class=\"wpcf7-form-control wpcf7-submit has-spinner button is-primary\" type=\"submit\" value=\"G\u00f6nder\" \/>\n\t\t<\/p>\n\t<\/div>\n<\/div>\n<p><span class=\"wpcf7-form-control-wrap\" data-name=\"textarea-947\"><textarea cols=\"40\" rows=\"10\" maxlength=\"2000\" class=\"wpcf7-form-control wpcf7-textarea wpcf7-calculator-result\" aria-invalid=\"false\" name=\"textarea-947\"><\/textarea><\/span>\n<\/p><p style=\"display: none !important;\" class=\"akismet-fields-container\" data-prefix=\"_wpcf7_ak_\"><label>&#916;<textarea name=\"_wpcf7_ak_hp_textarea\" cols=\"45\" rows=\"8\" maxlength=\"100\"><\/textarea><\/label><input type=\"hidden\" id=\"ak_js_1\" name=\"_wpcf7_ak_js\" value=\"22\"\/><script>document.getElementById( \"ak_js_1\" ).setAttribute( \"value\", ( new Date() ).getTime() );<\/script><\/p><div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div>\n<input type=\"hidden\" name=\"trp-form-language\" value=\"tr\"\/><\/form>\n<\/div>\n\r\n\t\t\t                <\/div>\r\n\t\t\t            <\/div>\r\n\t\t\t        <\/div><div class=\"formbox__actions_btns\"><div class=\"formbox__counters\"><div class=\"formbox__action-btn formbox__btn-count\" id=\"formbox-btn-count-434\">\r\n\t\t\t\t\t\t<span class=\"cb-icon-calculator\"><\/span> \r\n\t\t\t\t\t\t<span class=\"cb-number\" id=\"cb-count-434\">44<\/span>\r\n\t\t\t\t\t\t<span class=\"cb__tooltip\">Bug\u00fcn Kullan\u0131lan Hesaplama Say\u0131s\u0131<\/span>\r\n\t\t\t\t\t<\/div> \r\n\t\t\t\t\t<div class=\"formbox__footer-separate\">|<\/div>\r\n\t\t\t\t\t<button class=\"formbox__action-btn formbox__btn-likes\" id=\"formbox-btn-likes-434\">\r\n\t\t\t\t\t\t<span class=\"cb-icon-like\"><\/span> \r\n\t\t\t\t\t\t<span class=\"cb-number\" id=\"cb-like-434\">0<\/span>\r\n\t\t\t\t\t\t<span class=\"cb__tooltip\">Be\u011fen<\/span>\r\n\t\t\t\t\t<\/button>\r\n\t\t\t<\/div>\r\n            <style>\r\n                .mobile-add-button {display:none;}\r\n                .formbox__btn-share {display:flex;justify-content:flex-start;align-items:center;}\r\n                .mobile-add-button {display:none !important;}\r\n                @media(max-width: 768px) {\r\n                    .mobile-add-button {display:block !important;}\r\n                    .formbox__btn-share .mobile-hide-share{display:none !important;}\r\n                }\r\n            <\/style> \r\n                <div class=\"formbox__actions\">\r\n\t\t\t\t\t<button class=\"formbox__action-btn formbox__btn-link\" id=\"formbox-btn-link-434\">\r\n\t\t\t\t\t    <span class=\"cb-icon-link\"><\/span>\r\n\t\t\t\t\t    <span class=\"cb__tooltip\">Ba\u011flant\u0131y\u0131 Kopyala<\/span>\r\n\t\t\t\t\t<\/button>\r\n\t\t\t\t\t<div class=\"formbox__footer-separate\">|<\/div>\r\n\t\t\t\t\t<button class=\"formbox__action-btn formbox__btn-print\" name=\"cb_view\" value=\"434\">\r\n\t\t\t\t\t    <span class=\"cb-icon-print\"><\/span>\r\n\t\t\t\t\t    <span class=\"cb__tooltip\">Yazd\u0131r &amp; PDF<\/span>\r\n\t\t\t\t\t<\/button>\r\n                    <div class=\"formbox__footer-separate\">|<\/div>\r\n\t\t\t\t\t<a href=\"https:\/\/www.calculator6.com\/tr\/add-to-your-website\/?source=aWQ9Mzc2NCZsPXRyX1RS#widget-designer-tool\" style=\"text-decoration:none;\" class=\"formbox__action-btn formbox__btn-share\" name=\"cb_view\" data-value=\"434\">\r\n\t\t\t\t\t    <span class=\"mobile-add-button\">\r\n                            <svg style=\"width:23px;height:23px;\" enable-background=\"new 0 0 32 32\" height=\"32px\" id=\"svg2\" version=\"1.1\" viewbox=\"0 0 32 32\" width=\"32px\" xml:space=\"preserve\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:cc=\"http:\/\/creativecommons.org\/ns#\" xmlns:dc=\"http:\/\/purl.org\/dc\/elements\/1.1\/\" xmlns:inkscape=\"http:\/\/www.inkscape.org\/namespaces\/inkscape\" xmlns:rdf=\"http:\/\/www.w3.org\/1999\/02\/22-rdf-syntax-ns#\" xmlns:sodipodi=\"http:\/\/sodipodi.sourceforge.net\/DTD\/sodipodi-0.dtd\" xmlns:svg=\"http:\/\/www.w3.org\/2000\/svg\"><g id=\"background\"><rect fill=\"none\" height=\"32\" width=\"32\"\/><\/g><g id=\"sourcecode\"><polygon points=\"22,22 22,26 32,16 22,6 22,10 28,16  \"\/><polygon points=\"10,22 10,26 0,16 10,6 10,10 4,16  \"\/><polygon points=\"10,20 14,20 22,12 18,12  \"\/><\/g><\/svg>\r\n                        <\/span>\r\n                        <span class=\"mobile-hide-share\">Sitene Ekle<\/span>\r\n\t\t\t\t\t    <span id=\"addWebsiteModalTrigger\" class=\"cb__tooltip\"> Sitene Ekle<\/span>\r\n\t\t\t\t\t<\/a>\r\n\t\t\t\t<\/div><input type=\"hidden\" id=\"print_calculator_434\" name=\"print_calculator_434\" value=\"e8cadd7bee\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/tr\/wp-json\/wp\/v2\/posts\/3764\" \/><\/div><\/div><style id=\"calculator-434-custom-style\"><\/style><\/div>\n<hr \/>\n<h2>Fakt\u00f6riyel Nas\u0131l Hesaplan\u0131r?<\/h2>\n<p>Fakt\u00f6riyel hesaplama, pozitif bir tam say\u0131n\u0131n kendisiyle ve kendisinden k\u00fc\u00e7\u00fck t\u00fcm pozitif tam say\u0131larla \u00e7arp\u0131m\u0131n\u0131 ifade eden basit bir matematiksel i\u015flemdir. Fakt\u00f6riyel genellikle &quot;n!&quot; olarak g\u00f6sterilir ve &quot;n fakt\u00f6riyel&quot; olarak okunur. Ayr\u0131ca ba\u015fka yararl\u0131 matematik hesaplay\u0131c\u0131lar\u0131 da bulabilirsiniz <a href=\"https:\/\/www.calculator6.com\/tr\/math\/\">Burada<\/a>.<\/p>\n<p><strong>Fakt\u00f6riyel Hesaplama Ad\u0131mlar\u0131:<\/strong><\/p>\n<ol>\n<li><strong>Ba\u015flang\u0131\u00e7 de\u011feri:<\/strong><br \/>\nHesaplamak istedi\u011finiz say\u0131y\u0131 belirleyin. Bu say\u0131ya \u201cn\u201d diyelim.<\/li>\n<li><strong>\u00c7arpma i\u015flemi:<\/strong><br \/>\n\u201cn\u201d say\u0131s\u0131ndan ba\u015flayarak 1\u2019e kadar t\u00fcm pozitif tam say\u0131lar\u0131 \u00e7arp\u0131n.<br \/>\n\u00d6rne\u011fin n = 5: 5 i\u00e7in! = 5 x 4 x 3 x 2 x 1<\/li>\n<li><strong>Sonucun Bulunmas\u0131:<\/strong><br \/>\nT\u00fcm say\u0131lar\u0131n \u00e7arp\u0131lmas\u0131ndan sonra elde edilen sonu\u00e7 n fakt\u00f6riyeldir (n!).<br \/>\n\u00d6rne\u011fin, 5! = 5 x 4 x 3 x 2 x 1 = 120<\/li>\n<\/ol>\n<p><strong>Fakt\u00f6riyel Hesaplama \u00d6rnekleri:<\/strong><\/p>\n<ul>\n<li>3 Fakt\u00f6riyel (3!):<br \/>\n3! = 3 x 2 x 1 = 6<\/li>\n<li>4 Fakt\u00f6riyel (4!):<br \/>\n4! = 4 x 3 x 2 x 1 = 24<\/li>\n<li>5 Fakt\u00f6riyel (5!):<br \/>\n5! = 5 x 4 x 3 x 2 x 1 = 120<\/li>\n<\/ul>\n<h3>Fakt\u00f6riyel Nedir?<\/h3>\n<p>Fakt\u00f6riyel, matematikte pozitif bir tam say\u0131n\u0131n kendisiyle ve kendisinden k\u00fc\u00e7\u00fck t\u00fcm pozitif tam say\u0131lar\u0131n \u00e7arp\u0131m\u0131n\u0131 ifade eden bir i\u015flemdir. Fakt\u00f6riyel \u201cn!\u201d sembol\u00fcyle g\u00f6sterilir. ve \u201cn fakt\u00f6riyel\u201d olarak okunur.<\/p>\n<p>Fakt\u00f6riyel pozitif tam say\u0131lar\u0131n \u00e7arp\u0131m\u0131 olarak tan\u0131mlan\u0131r. \u00d6rne\u011fin, n pozitif bir tam say\u0131 oldu\u011fundan, fakt\u00f6riyel n (n!) \u015fu \u015fekilde hesaplan\u0131r:<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\" data-no-translation=\"\" data-no-auto-translation=\"\">n! = n \u00d7 (n - 1) \u00d7 (n - 2) \u00d7 ... \u00d7 2 \u00d7 1<\/span>\n<p>0 fakt\u00f6riyel (0!) \u00f6zel tan\u0131m olarak 1&#039;e e\u015fittir. Bu tan\u0131m matematiksel i\u015flemlere kolayl\u0131k sa\u011flamak amac\u0131yla benimsenmi\u015ftir.<\/p>\n<p>Basit \u00e7arpman\u0131n \u00f6tesinde, fakt\u00f6riyel \u00e7ok \u00e7e\u015fitli matematiksel problemleri \u00e7\u00f6zmede temel bir rol oynar. B\u00fcy\u00fck say\u0131larla \u00e7al\u0131\u015f\u0131rken fakt\u00f6riyel hesaplamalar\u0131 zor olabilir, bu nedenle fakt\u00f6riyel hesaplay\u0131c\u0131lar\u0131 kullanmak yayg\u0131nd\u0131r. Fakt\u00f6riyelleri yayg\u0131n olarak kullanan kombinatorik hakk\u0131nda daha fazla bilgi i\u00e7in.<\/p>\n<h3><strong>Fakt\u00f6riyel Hesap Makinesi Kullan\u0131mlar\u0131<\/strong><\/h3>\n<ul>\n<li>Matematik ve \u0130statistik: Olas\u0131l\u0131k ve istatistiksel analiz i\u00e7in perm\u00fctasyon ve kombinasyonlar\u0131n hesaplanmas\u0131.<\/li>\n<li>Bilgisayar Bilimi: Algoritmalar\u0131n, \u00f6zellikle \u00f6zyinelemeli fonksiyonlarda ve dinamik programlamada karma\u015f\u0131kl\u0131\u011f\u0131n\u0131n belirlenmesi.<\/li>\n<li>M\u00fchendislik: Operasyonel ara\u015ft\u0131rma ve optimizasyonda problem \u00e7\u00f6zme.<\/li>\n<li>Fizik: Kuantum mekani\u011fi ve istatistiksel mekanikte fakt\u00f6riyel terimlerinin hesaplanmas\u0131.<\/li>\n<li>Finans: Karma\u015f\u0131k finansal senaryolar\u0131n ve risk de\u011ferlendirmelerinin modellenmesi.<\/li>\n<li>Biyoloji: Genetik dizilerin analizi ve pop\u00fclasyon geneti\u011fi.<\/li>\n<li>Kimya: Molek\u00fcllerin ka\u00e7 farkl\u0131 \u015fekilde d\u00fczenlenebilece\u011finin hesaplanmas\u0131.<\/li>\n<li>Kriptografi: \u015eifreleme algoritmalar\u0131 i\u00e7in b\u00fcy\u00fck fakt\u00f6riyel tabanl\u0131 anahtarlar\u0131n \u00fcretilmesi.<\/li>\n<li>Oyun Geli\u015ftirme: Prosed\u00fcrel i\u00e7erik olu\u015fturma ve olas\u0131 oyun durumlar\u0131n\u0131 hesaplama.<\/li>\n<li>E\u011fitim: \u00d6\u011frencilere fakt\u00f6riyel kavramlar\u0131n\u0131 ve ger\u00e7ek d\u00fcnya problemlerindeki uygulamalar\u0131n\u0131 \u00f6\u011fretmek.<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Fakt\u00f6riyel hesaplay\u0131c\u0131, belirli bir say\u0131n\u0131n fakt\u00f6riyelini h\u0131zl\u0131 ve do\u011fru bir \u015fekilde hesaplaman\u0131za olanak tan\u0131yan bir ara\u00e7t\u0131r.<\/p>","protected":false},"author":1,"featured_media":3768,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[54],"tags":[],"class_list":["post-3764","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/posts\/3764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/comments?post=3764"}],"version-history":[{"count":11,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/posts\/3764\/revisions"}],"predecessor-version":[{"id":3784,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/posts\/3764\/revisions\/3784"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/media\/3768"}],"wp:attachment":[{"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/media?parent=3764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/categories?post=3764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.calculator6.com\/tr\/wp-json\/wp\/v2\/tags?post=3764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}