{"id":63,"date":"2023-09-17T07:21:09","date_gmt":"2023-09-17T07:21:09","guid":{"rendered":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/"},"modified":"2023-09-17T07:21:09","modified_gmt":"2023-09-17T07:21:09","slug":"funcao-fatorial-de-um-numero","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/","title":{"rendered":"Fun\u00e7\u00e3o fatorial de um n\u00famero"},"content":{"rendered":"<p>Esta p\u00e1gina explica o que \u00e9 o fatorial de um n\u00famero e como ele \u00e9 calculado. Al\u00e9m disso, s\u00e3o apresentados diversos exemplos e uma tabela com os valores dos fatoriais mais utilizados. Tamb\u00e9m ensina como calcular o fatorial de um n\u00famero com a calculadora. E, finalmente, s\u00e3o ilustradas as aplica\u00e7\u00f5es e propriedades dos fatoriais. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-factorial-de-un-numero\"><\/span> Qual \u00e9 o fatorial de um n\u00famero? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Em matem\u00e1tica, o <strong>fatorial de um n\u00famero<\/strong> \u00e9 igual ao produto de todos os inteiros positivos de 1 at\u00e9 esse n\u00famero. Al\u00e9m disso, o fatorial de um n\u00famero \u00e9 representado por um ponto de exclama\u00e7\u00e3o (!) ap\u00f3s o n\u00famero. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/factorielle-dun-nombre.jpg\" alt=\"fatorial de um n\u00famero\" class=\"wp-image-1870\" width=\"152\" height=\"152\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Por exemplo, para determinar o fatorial do n\u00famero <em>n<\/em> , tamb\u00e9m chamado de fatorial <em>n<\/em> , deve-se multiplicar o n\u00famero <em>n<\/em> por todos os inteiros que o precedem (come\u00e7ando por um): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49a90a973e9e420c44502cd9c8a870ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! = 1 \\cdot 2 \\cdot 3 \\cdots (n-2) \\cdot (n-1) \\cdot n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"265\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-calcular-el-factorial-de-un-numero\"><\/span> Como calcular o fatorial de um n\u00famero<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos o significado do fatorial de um n\u00famero, vamos ver com um exemplo como determinar qualquer fatorial:<\/p>\n<ul>\n<li> Calcule o fatorial de 4:<\/li>\n<\/ul>\n<p> Como vimos na sua defini\u00e7\u00e3o matem\u00e1tica, o fatorial de um n\u00famero equivale \u00e0 multiplica\u00e7\u00e3o de todos os inteiros positivos menores ou iguais a ele. Portanto, para calcular o fatorial de 4, precisamos multiplicar os n\u00fameros 1, 2, 3 e 4:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2d8186d4343b8a2ffc6567e323dab6d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4! = 1 \\cdot 2 \\cdot 3 \\cdot 4 =24\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"153\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> O fatorial de 4, portanto, d\u00e1 24. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-factoriales-de-numeros\"><\/span> Exemplos de fatoriais de n\u00fameros<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o da no\u00e7\u00e3o de fatorial de um n\u00famero, deixamos um exemplo de c\u00e1lculo de v\u00e1rios fatoriais de n\u00fameros diferentes:<\/p>\n<ul>\n<li> Fatorial de 3:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-325e737422d7201e476c4a60bfe966f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3! = 1 \\cdot 2 \\cdot 3 =6\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Fatorial de 5:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b9936934f623ae1f84b1d8d33b5a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5! = 1 \\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5=120\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Fatorial de 6:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bb40997fdc483ae843ffed87eb17a70c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6! = 1 \\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5 \\cdot 6=720\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"205\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Fatorial de 1:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78b2257245ff53ae4369f3b71629ae83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1! = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Logicamente, o fatorial do n\u00famero 1 \u00e9 igual a 1, pois basta multiplicar 1.<\/p>\n<ul>\n<li> Fatorial de 0:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-255b29d39824041f4d334887daa9d55d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0! = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sim, tudo bem, surpreendentemente, o fatorial de 0 n\u00e3o \u00e9 igual a zero, mas sim a 1. Isso pode lhe parecer um pouco estranho, pois em teoria voc\u00ea tem que multiplicar 0 por 1. Por\u00e9m, \u00e9 adotado por conven\u00e7\u00e3o que 0! =1 porque a <a href=\"https:\/\/es.wikipedia.org\/wiki\/Producto_vac%C3%ADo\" target=\"_blank\" rel=\"noreferrer noopener\">propriedade do produto est\u00e1 vazia<\/a> . Deixamos este link caso voc\u00ea queira saber mais, embora n\u00e3o seja muito relevante que voc\u00ea saiba o motivo, o importante \u00e9 que voc\u00ea lembre que <strong>o fatorial de 0 \u00e9 igual a 1<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Lista-de-resultados-de-factoriales-de-numeros\"><\/span> Lista de resultados para fatoriais de n\u00fameros<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Abaixo resumimos os fatoriais dos n\u00fameros mais usados em uma tabela, para que voc\u00ea n\u00e3o precise calcul\u00e1-los manualmente. <\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\"> O n\u00famero<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\"> Fatorial do n\u00famero<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 24<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 120<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 720<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 7<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5.040<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 8<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 40.320<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 362.880<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> dez<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 3.628.800<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> onze<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 39.916.800<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 12<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 479.001.600<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 13<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6.227.020.800<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 14<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 87 178 291 200<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> quinze<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1.307.674.368.000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 16<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 20.922.789.888.000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 17<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 355.687.428.096.000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 18<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6.402.373.705.728.000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 19<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 121.645.100.408.832.000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> vinte<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2.432.902.008 176.640.000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> cinquenta<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 3.041.409.320 \u00b7 <sup>10,64<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 100<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9.332 621.544 \u00b7 <sup>10.157<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1.000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4.023.872.601 \u00b7 <sup>10.2567<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 10.000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2.846.259.681 \u00b7 <sup>10.35.659<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 100.000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2 824 229 408 \u00b7 10 <sup>45 6573<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1.000.000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 8.263.931.688 \u00b7 10 <sup>5.565.708<\/sup> <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Factorial-de-un-numero-con-la-calculadora\"><\/span> Fatorial de um n\u00famero com a calculadora<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Como voc\u00ea pode ver nos exemplos anteriores, os resultados dos fatoriais de dois n\u00fameros consecutivos aumentam exponencialmente, por isso \u00e9 bastante dif\u00edcil conhecer o fatorial de n\u00fameros grandes. Ent\u00e3o mostraremos como encontrar o fatorial de um n\u00famero com a calculadora.<\/p>\n<p> As calculadoras cient\u00edficas possuem uma chave com o <em>s\u00edmbolo x!<\/em> ou <em>n\u00e3o!<\/em> que \u00e9 usado para calcular o fatorial de um n\u00famero inteiro. Ent\u00e3o, para determinar quanto vale um fatorial, voc\u00ea deve realizar a seguinte sequ\u00eancia na calculadora:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c202f31b798e218ed65210a5eaff6293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! \\quad \\color{red} \\bm{\\longrightarrow} \\quad \\color{black} n\\rightarrow \\boxed{x!} \\rightarrow \\boxed{=}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"263\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Normalmente, as calculadoras CASIO possuem a <em><em>chave fatorial x!<\/em> ou <em>n\u00e3o!<\/em><\/em> acima do bot\u00e3o <em>x <sup>-1<\/sup><\/em> .<\/p>\n<p> Como exemplo, resolveremos um fatorial com a calculadora para que voc\u00ea verifique se sabe como faz\u00ea-lo. Por exemplo, faremos o fatorial de 9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-797b93b341570c99b6ae23521134b3e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"9! \\quad \\color{red} \\bm{\\longrightarrow} \\quad \\color{black} 9\\rightarrow \\boxed{x!} \\rightarrow \\boxed{=} \\rightarrow 362880\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"340\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Para encontrar o fatorial de 9 voc\u00ea deve primeiro inserir o n\u00famero 9 e depois pressionar a tecla<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6e5326c9702600ee8b6727dc5e449b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{x!}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"27\" style=\"vertical-align: -6px;\"><\/p>\n<p> e por fim, pressione o bot\u00e3o igual. Neste caso, a calculadora dever\u00e1 nos mostrar o resultado de 362.880. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aplicaciones-del-numero-factorial\"><\/span> Aplica\u00e7\u00f5es do n\u00famero fatorial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A fun\u00e7\u00e3o fatorial de um n\u00famero pode parecer uma opera\u00e7\u00e3o muito simples e absurda, mas em \u00e1lgebra avan\u00e7ada ela \u00e9 bastante utilizada. Veremos ent\u00e3o os principais usos do fatorial.<\/p>\n<p> Em primeiro lugar, o fatorial \u00e9 uma opera\u00e7\u00e3o essencial para o c\u00e1lculo de um <a href=\"https:\/\/mathority.org\/pt\/propriedades-do-coeficiente-binomial-de-numero-combinatorio\/\"><strong><span style=\"text-decoration: underline;\">n\u00famero combinat\u00f3rio<\/span><\/strong><\/a> , uma opera\u00e7\u00e3o mais que particular. Se voc\u00ea n\u00e3o sabe o que \u00e9 o n\u00famero combinat\u00f3rio, pode ver em que consiste e como \u00e9 calculado neste link, onde encontrar\u00e1 exemplos, exerc\u00edcios resolvidos e quais s\u00e3o suas propriedades. Al\u00e9m disso, voc\u00ea poder\u00e1 ver para que ele \u00e9 usado, pois possui muitas aplica\u00e7\u00f5es no mundo real.<\/p>\n<p> O fatorial tamb\u00e9m \u00e9 usado em matem\u00e1tica para determinar o polin\u00f4mio de Taylor de uma fun\u00e7\u00e3o.<\/p>\n<p> Da mesma forma, o fatorial \u00e9 utilizado para resolver certos problemas combinat\u00f3rios, em particular para calcular combina\u00e7\u00f5es e permuta\u00e7\u00f5es. Nesse sentido, os fatoriais tamb\u00e9m s\u00e3o frequentemente usados para calcular probabilidades por meio de combinat\u00f3ria.<\/p>\n<p> Uma permuta\u00e7\u00e3o de n elementos corresponde a cada um dos diferentes arranjos que podem ser feitos com estes elementos. Portanto, para calcular uma permuta\u00e7\u00e3o, utiliza-se o fatorial. Por exemplo, se em um problema voc\u00ea quiser encontrar o n\u00famero de possibilidades em que 7 objetos podem ser organizados, dever\u00e1 calcular o fatorial de 7.<\/p>\n<p> Agora vamos ver um exerc\u00edcio resolvido:<\/p>\n<ul>\n<li> Temos 5 pares de sapatos diferentes, de quantas maneiras podemos organiz\u00e1-los?<\/li>\n<\/ul>\n<p> Neste exerc\u00edcio temos que descobrir todas as formas poss\u00edveis de combinar estes 5 pares de sapatos tendo em conta a ordem em que os colocamos. Ent\u00e3o para resolver o problema basta calcular o fatorial de 5:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6725f02a218ddc6ac88f42df99e13261_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5! = 1\\cdot 2 \\cdot 3\\cdot 4\\cdot 5 =120\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Resumindo, os 5 pares de sapatos podem ser colocados de 120 maneiras diferentes.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-del-numero-factorial\"><\/span> Propriedades do n\u00famero fatorial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O n\u00famero fatorial possui as seguintes caracter\u00edsticas:<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Sendo dois inteiros positivos <em>n<\/em> e <em>m<\/em> tais que <em>n<\/em> \u00e9 maior que <em>m<\/em> , ent\u00e3o, obviamente, o valor do fatorial de <em>n<\/em> \u00e9 maior que o valor do fatorial de <em>m<\/em> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e858d82412bf78abe42397373dc67e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>m \\quad \\longrightarrow \\quad n! > m!&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;15&#8243; width=&#8221;183&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">O fatorial de um n\u00famero pode ser decomposto fatorialmente de modo que um dos fatores seja o fatorial de um n\u00famero menor.<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37ca3a1bea020ccbff019c2e1766be93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>m \\quad \\longrightarrow \\quad n!= n\\cdot (n-1) \\cdots (m+1)\\cdot m!&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;361&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> Por exemplo, 6 \u00e9 maior que 4, ent\u00e3o a express\u00e3o para o fatorial de 6 pode ser simplificada da seguinte forma:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ca24a5de3e3cad7df5fc66d694e6eee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6! = 6 \\cdot 5 \\cdot 4!\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">A seguinte express\u00e3o alg\u00e9brica \u00e9 v\u00e1lida para o fatorial de qualquer n\u00famero, exceto o fatorial de 1:<\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35dd01cda41e2b84fbf524ff6632b4f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n!< \\left( \\frac{n+1}{2} \\right)^n\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"118\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Factorial-de-un-numero-negativo-o-decimal\"><\/span> Fatorial de um n\u00famero negativo ou decimal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Acabamos de ver como determinar o valor do fatorial de um n\u00famero inteiro positivo, mas\u2026 podemos calcular o fatorial de um n\u00famero negativo ou de um n\u00famero decimal? A resposta \u00e9 sim, mas \u00e9 necess\u00e1rio conhecimento avan\u00e7ado de matem\u00e1tica.<\/p>\n<p> O fatorial de um n\u00famero negativo e de um n\u00famero decimal \u00e9 calculado usando uma fun\u00e7\u00e3o especial chamada \u201cfun\u00e7\u00e3o gama\u201d de Euler, que \u00e9 definida pela seguinte integral:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20553bef4090def5334022fbbd8f646b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Gamma(z)=\\int_0^\\infty t^{z-1} e^{-t}\\, \\mathrm{d}t\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"168\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Assim, qualquer tipo de fatorial pode ser resolvido com a fun\u00e7\u00e3o Gamma porque a seguinte equa\u00e7\u00e3o \u00e9 sempre verdadeira:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d336cefb8a14d587ad508fcde7c55914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! = \\Gamma(n+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, para encontrar o fatorial de 0,5, por exemplo, devemos encontrar o valor de<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74cf80cb3a1094ad541acd2fadab6c93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Gamma(1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -5px;\"><\/p>\n<p> porque:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b2359c9eadbef6aad92eb84450a4165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,5! = \\Gamma(0,5+1) =\\Gamma(1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E a solu\u00e7\u00e3o da integral corresponder\u00e1 ao fatorial de 0,5.<\/p>\n<p> Obviamente resolver a integral da fun\u00e7\u00e3o Gama n\u00e3o \u00e9 f\u00e1cil e n\u00e3o iremos ensin\u00e1-la neste artigo, pois muitos conceitos matem\u00e1ticos teriam que ser explicados previamente. Mas quer\u00edamos que voc\u00ea soubesse que existe a possibilidade de calcular o fatorial de um n\u00famero negativo ou de um n\u00famero decimal.<\/p>\n<p> Na verdade, como exemplo, calculamos alguns valores fatoriais e decimais negativos: <\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7ad27047f682b1254c792b678fc5fdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\underline{\\bm{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: -3px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b827a8ed6060949fe26a6587d7f0967a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\underline{\\bm{n!}}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1d9404653c812c40471f884311057d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{1}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"40\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23d859aa265b7e809f660f3044c24290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}\\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"37\" style=\"vertical-align: -12px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a19589a09d32e0a6528c6504a6011606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(-\\frac{1}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"54\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdb20bafedd2cc451408e573c7e9d3c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"25\" style=\"vertical-align: -3px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fb86f24adb23da02e1f18f7d06c4e851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{3}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"40\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cbc4e85460f947ab1d92294e3847264e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{4}\\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"37\" style=\"vertical-align: -12px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-973e06c4da8ee3607e1e8f94a7a7bf4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{5}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"40\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c675261e5e335903926dc229dae84d9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{15}{8}\\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Esta p\u00e1gina explica o que \u00e9 o fatorial de um n\u00famero e como ele \u00e9 calculado. Al\u00e9m disso, s\u00e3o apresentados diversos exemplos e uma tabela com os valores dos fatoriais mais utilizados. Tamb\u00e9m ensina como calcular o fatorial de um n\u00famero com a calculadora. E, finalmente, s\u00e3o ilustradas as aplica\u00e7\u00f5es e propriedades dos fatoriais. Qual &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\"> <span class=\"screen-reader-text\">Fun\u00e7\u00e3o fatorial de um n\u00famero<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-63","post","type-post","status-publish","format-standard","hentry","category-binomios"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Fatorial de um n\u00famero: o que \u00e9 e como calcul\u00e1-lo \u2705<\/title>\n<meta name=\"description\" content=\"Tudo sobre o fatorial de um n\u00famero: o que \u00e9, como calcul\u00e1-lo, exemplos, tabela com fatoriais grandes, c\u00e1lculo com calculadora, propriedades, aplica\u00e7\u00f5es,...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Fatorial de um n\u00famero: o que \u00e9 e como calcul\u00e1-lo \u2705\" \/>\n<meta property=\"og:description\" content=\"Tudo sobre o fatorial de um n\u00famero: o que \u00e9, como calcul\u00e1-lo, exemplos, tabela com fatoriais grandes, c\u00e1lculo com calculadora, propriedades, aplica\u00e7\u00f5es,...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T07:21:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/factorielle-dun-nombre.jpg\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Fun\u00e7\u00e3o fatorial de um n\u00famero\",\"datePublished\":\"2023-09-17T07:21:09+00:00\",\"dateModified\":\"2023-09-17T07:21:09+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\"},\"wordCount\":1159,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Bin\u00f4mios\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\",\"url\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\",\"name\":\"\u25b7 Fatorial de um n\u00famero: o que \u00e9 e como calcul\u00e1-lo \u2705\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-09-17T07:21:09+00:00\",\"dateModified\":\"2023-09-17T07:21:09+00:00\",\"description\":\"Tudo sobre o fatorial de um n\u00famero: o que \u00e9, como calcul\u00e1-lo, exemplos, tabela com fatoriais grandes, c\u00e1lculo com calculadora, propriedades, aplica\u00e7\u00f5es,...\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Fun\u00e7\u00e3o fatorial de um n\u00famero\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 Fatorial de um n\u00famero: o que \u00e9 e como calcul\u00e1-lo \u2705","description":"Tudo sobre o fatorial de um n\u00famero: o que \u00e9, como calcul\u00e1-lo, exemplos, tabela com fatoriais grandes, c\u00e1lculo com calculadora, propriedades, aplica\u00e7\u00f5es,...","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/","og_locale":"pt_BR","og_type":"article","og_title":"\u25b7 Fatorial de um n\u00famero: o que \u00e9 e como calcul\u00e1-lo \u2705","og_description":"Tudo sobre o fatorial de um n\u00famero: o que \u00e9, como calcul\u00e1-lo, exemplos, tabela com fatoriais grandes, c\u00e1lculo com calculadora, propriedades, aplica\u00e7\u00f5es,...","og_url":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/","article_published_time":"2023-09-17T07:21:09+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/factorielle-dun-nombre.jpg"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"6 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Fun\u00e7\u00e3o fatorial de um n\u00famero","datePublished":"2023-09-17T07:21:09+00:00","dateModified":"2023-09-17T07:21:09+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/"},"wordCount":1159,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Bin\u00f4mios"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/","url":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/","name":"\u25b7 Fatorial de um n\u00famero: o que \u00e9 e como calcul\u00e1-lo \u2705","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/#website"},"datePublished":"2023-09-17T07:21:09+00:00","dateModified":"2023-09-17T07:21:09+00:00","description":"Tudo sobre o fatorial de um n\u00famero: o que \u00e9, como calcul\u00e1-lo, exemplos, tabela com fatoriais grandes, c\u00e1lculo com calculadora, propriedades, aplica\u00e7\u00f5es,...","breadcrumb":{"@id":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/pt\/funcao-fatorial-de-um-numero\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Fun\u00e7\u00e3o fatorial de um n\u00famero"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/pt\/#website","url":"https:\/\/mathority.org\/pt\/","name":"Mathority","description":"Onde a curiosidade encontra o c\u00e1lculo!","publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/mathority.org\/pt\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/pt\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00","name":"Equipe Mathoridade","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Equipe Mathoridade"},"sameAs":["http:\/\/mathority.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/63","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/comments?post=63"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/63\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/media?parent=63"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/categories?post=63"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/tags?post=63"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}