{"id":4171,"date":"2026-11-02T10:05:03","date_gmt":"2026-11-02T10:05:03","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/carpan-hesaplama\/"},"modified":"2026-11-02T10:05:03","modified_gmt":"2026-11-02T10:05:03","slug":"carpan-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/carpan-hesaplama\/","title":{"rendered":"\u00c7arpan Hesaplama \u2013 Bir Say\u0131n\u0131n T\u00fcm \u00c7arpanlar\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">T\u00fcm \u00e7arpanlar\u0131, \u00e7arpan \u00e7iftlerini ve asal \u00e7arpanlara ayr\u0131m\u0131 bulun<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4171\" data-favorite-title=\"\u00c7arpanlar\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/carpan-hesaplama\/\" data-favorite-excerpt=\"1 ile 10\u00b9\u00b2 aras\u0131nda herhangi bir tam say\u0131 girin; t\u00fcm \u00e7arpanlar\u0131n\u0131, \u00e7arpan (b\u00f6len) say\u0131s\u0131n\u0131 ve toplam\u0131n\u0131, asal \u00e7arpanlara ayr\u0131m\u0131n\u0131, \u00e7arpan ikililerini ve say\u0131n\u0131n asal, m\u00fckemmel, art\u0131kl\u0131 m\u0131 eksik mi oldu\u011funu an\u0131nda g\u00f6r\u00fcn \u2014 ya da 2\u20135 say\u0131y\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131p ortak \u00e7arpanlar\u0131n\u0131 ve EBOB&#039;lar\u0131n\u0131 bulun.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-arithmetic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/carpan-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4171\" data-post=\"4171\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Mod<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"mod\"><option value=\"single\" selected>All factors of one number<\/option><option value=\"common\">2\u20135 say\u0131n\u0131n ortak \u00e7arpanlar\u0131<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Say\u0131 (n)<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"say_n\" id=\"field-2\" aria-describedby=\"calc-info-2\" min=\"-1000000000000\" max=\"1000000000000\" step=\"1\" value=\"360\"\/><small id=\"calc-info-2\">1 ile 10\u00b9\u00b2 (10.000.000.000.000) aras\u0131nda bir tam say\u0131. Eksi i\u015fareti kullan\u0131labilir \u2014 |n| de\u011ferinin \u00e7arpanlar\u0131 listelenir ve negatif \u00e7arpanlar belirtilir.<\/small><\/div><div class=\"field is-single\" id=\"input-3\" hidden><label for=\"field-3\">Say\u0131lar<\/label><textarea id=\"field-3\" name=\"saylar\">12, 18, 30<\/textarea><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4171\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>T\u00fcm \u00e7arpanlar<\/span><span class=\"result-term\">d<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>\u00c7arpan say\u0131s\u0131<\/span><span class=\"result-term\">\u03c4(n)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>\u00c7arpanlar\u0131n toplam\u0131<\/span><span class=\"result-term\">\u03c3(n)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Asal \u00e7arpanlara ay\u0131rma<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>\u00c7arpan \u00e7iftleri (a \u00d7 b = n)<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-6\"><span class=\"field-title\"><span>Asal m\u0131, m\u00fckemmel mi, bol mu, eksik mi?<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-7\"><span class=\"field-title\"><span>Ortak \u00e7arpanlar ve EBOB<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4171\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>\u00c7arpan form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ d \\text{, } n \\text{ say\u0131s\u0131n\u0131n bir \u00e7arpan\u0131d\u0131r} \\iff n = d \\cdot k \\text{, burada } k \\text{ bir tam say\u0131d\u0131r} \\]\n\\[ n = p_1^{e_1} \\cdot p_2^{e_2} \\cdots p_r^{e_r} \\;\\Rightarrow\\; \\tau(n) = \\prod_{i=1}^{r} (e_i + 1), \\qquad \\sigma(n) = \\prod_{i=1}^{r} \\frac{p_i^{e_i + 1} - 1}{p_i - 1} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>G\u00f6sterimler:<\/strong><\/p>\n<ul>\n<li>\\(d\\) \u2014 \\(n\\)'in bir \u00e7arpan\u0131 (b\u00f6leni)<\/li>\n<li>\\(n\\) \u2014 \u00e7arpanlar\u0131na ayr\u0131lacak say\u0131<\/li>\n<li>\\(p_i\\), \\(e_i\\) \u2014 \\(n\\)'in birbirinden farkl\u0131 asal \u00e7arpanlar\u0131 ve bunlar\u0131n asal \u00e7arpanlara ay\u0131rmadaki \u00fcsleri<\/li>\n<li>\\(\\tau(n)\\) \u2014 \\(n\\)'in t\u00fcm \u00e7arpanlar\u0131n\u0131n say\u0131s\u0131<\/li>\n<li>\\(\\sigma(n)\\) \u2014 \\(n\\)'in t\u00fcm \u00e7arpanlar\u0131n\u0131n toplam\u0131<\/li>\n<\/ul>\n<p>\u0130lk sat\u0131r \u00e7arpan\u0131n tan\u0131m\u0131d\u0131r: \\(d\\) say\u0131s\u0131 \\(n\\)'yi kalans\u0131z olarak tam b\u00f6ler. \u0130kinci sat\u0131r ise asal \u00e7arpanlara ay\u0131rman\u0131n hem ka\u00e7 \u00e7arpan bulundu\u011funu hem de bu \u00e7arpanlar\u0131n toplam\u0131n\u0131 nas\u0131l belirledi\u011fini g\u00f6sterir.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>\u00c7arpanlar \u2013 \u00f6rnek hesaplama<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> arac\u0131n varsay\u0131lan de\u011feri olan \\(n = 360\\)'\u0131n t\u00fcm \u00e7arpanlar\u0131n\u0131 bulal\u0131m.<\/p>\n<p>\\[ 360 = 2^3 \\cdot 3^2 \\cdot 5 \\]<\/p>\n<p>\\[ \\tau(360) = (3+1)(2+1)(1+1) = 24 \\]<\/p>\n<p>\\[ \\sigma(360) = \\frac{2^4 - 1}{2 - 1} \\cdot \\frac{3^3 - 1}{3 - 1} \\cdot \\frac{5^2 - 1}{5 - 1} = 15 \\cdot 13 \\cdot 6 = 1170 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> 360'\u0131n <strong>24 \u00e7arpan\u0131<\/strong> vard\u0131r: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Bu \u00e7arpanlar\u0131n toplam\u0131 <strong>1170<\/strong>'tir. Ger\u00e7ek b\u00f6lenlerin toplam\u0131 \\(1170 - 360 = 810 &gt; 360\\) oldu\u011fundan 360 <strong>art\u0131kl\u0131<\/strong> bir say\u0131d\u0131r. \u00c7arpanlar \\(1 \\times 360\\)'dan \\(18 \\times 20\\)'ye kadar uzanan 12 ikili olu\u015fturur.<\/p>\n<p>\n\r\n<\/section>\n<h2>\u00c7arpan hesaplama arac\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Mod<\/strong> se\u00e7in: <em>Tek bir say\u0131n\u0131n t\u00fcm \u00e7arpanlar\u0131<\/em> ya da <em>2\u20135 say\u0131n\u0131n ortak \u00e7arpanlar\u0131<\/em>.<\/li>\n<li><em>T\u00fcm \u00e7arpanlar<\/em> modunda <strong>Say\u0131 (n)<\/strong> alan\u0131na 1 ile 10\u00b9\u00b2 aras\u0131nda bir tam say\u0131 yaz\u0131n. Eksi i\u015fareti de kabul edilir; ara\u00e7 \\(|n|\\)'in \u00e7arpanlar\u0131n\u0131 listeler ve negatif olanlar\u0131 da belirtir.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: k\u00fc\u00e7\u00fckten b\u00fcy\u00fc\u011fe <strong>T\u00fcm \u00e7arpanlar<\/strong>, <strong>\u00c7arpan say\u0131s\u0131<\/strong> \\(\\tau(n)\\), <strong>\u00c7arpanlar\u0131n toplam\u0131<\/strong> \\(\\sigma(n)\\), <strong>Asal \u00e7arpanlara ay\u0131rma<\/strong>, <strong>\u00c7arpan ikilileri<\/strong> tablosu ve say\u0131n\u0131n asal, m\u00fckemmel, art\u0131kl\u0131 ya da eksik oldu\u011funa dair s\u0131n\u0131fland\u0131rma.<\/li>\n<li><em>Ortak \u00e7arpanlar<\/em> modunda <strong>Say\u0131lar<\/strong> kutusuna virg\u00fcl, bo\u015fluk, noktal\u0131 virg\u00fcl ya da sat\u0131r sonuyla ayr\u0131lm\u0131\u015f 2\u20135 s\u0131f\u0131rdan farkl\u0131 tam say\u0131 girin (\u00f6rne\u011fin <code>12, 18, 30<\/code>). Sonu\u00e7ta say\u0131lar\u0131n payla\u015ft\u0131\u011f\u0131 t\u00fcm \u00e7arpanlar listelenir ve <strong>en b\u00fcy\u00fck ortak b\u00f6len<\/strong> vurgulan\u0131r.<\/li>\n<\/ol>\n<h2>\u00c7arpan nedir ve neden \u00f6nemlidir?<\/h2>\n<p>\\(n\\) say\u0131s\u0131n\u0131n bir <strong>\u00e7arpan\u0131<\/strong>, \\(n\\)'yi kalans\u0131z b\u00f6lebilen her tam say\u0131d\u0131r. \u00d6rne\u011fin 12; 1, 2, 3, 4, 6 ve 12'ye tam b\u00f6l\u00fcn\u00fcr, dolay\u0131s\u0131yla \u00e7arpanlar\u0131 bunlard\u0131r. \\(n\\)'in her \\(d\\) \u00e7arpan\u0131n\u0131n bir e\u015fi vard\u0131r: \\(n = d \\times k\\) oldu\u011fundan e\u015f, \\(k = n \\div d\\) say\u0131s\u0131d\u0131r. Bu y\u00fczden \u00e7arpanlar kendili\u011finden <em>\u00e7arpan ikilileri<\/em> bi\u00e7iminde d\u00fczenlenir. \\(6 \\times 6\\) ikilisine sahip 36 gibi tam kare bir say\u0131n\u0131n \u00e7arpan say\u0131s\u0131 tektir, \u00e7\u00fcnk\u00fc \\(\\sqrt{n}\\) kendisiyle e\u015fle\u015fir.<\/p>\n<p>B\u00fcy\u00fck bir say\u0131n\u0131n t\u00fcm \u00e7arpanlar\u0131n\u0131 bulman\u0131n en h\u0131zl\u0131 yolu <strong>asal \u00e7arpanlara ay\u0131rmad\u0131r<\/strong>. \\(n = p_1^{e_1} \\cdot p_2^{e_2} \\cdots p_r^{e_r}\\) ise her \u00e7arpan, ayn\u0131 asallar\u0131n en \u00e7ok \\(e_i\\) \u00fcsle kurulmu\u015f bir \u00e7arp\u0131m\u0131d\u0131r. \u00c7arpan say\u0131s\u0131 buradan hemen \u00e7\u0131kar: \\(\\tau(n) = (e_1+1)(e_2+1)\\cdots(e_r+1)\\). Ad\u0131m ad\u0131m asal \u00e7arpanlara ay\u0131rma i\u00e7in <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-factorization-calculator\/\">Asal \u00c7arpanlara Ay\u0131rma Hesaplay\u0131c\u0131s\u0131<\/a>'na bak\u0131n; tek bir aday\u0131 s\u0131namak i\u00e7inse <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/asal-sayi-kontrolu\/\">Asal Say\u0131 Testi<\/a> daha h\u0131zl\u0131d\u0131r.<\/p>\n<p>\u00c7arpanlar\u0131n toplam\u0131 \\(\\sigma(n)\\) salt bir merak konusu de\u011fildir; say\u0131y\u0131 s\u0131n\u0131fland\u0131r\u0131r. Ger\u00e7ek b\u00f6lenlerin (say\u0131n\u0131n kendisi hari\u00e7 t\u00fcm \u00e7arpanlar\u0131n) toplam\u0131 tam olarak \\(n\\)'e e\u015fitse say\u0131 <strong>m\u00fckemmel<\/strong>dir, 6 ve 28 gibi. Toplam daha fazlaysa say\u0131 <strong>art\u0131kl\u0131<\/strong>, daha azsa <strong>eksik<\/strong> say\u0131l\u0131r. Asal say\u0131lar\u0131n tek ger\u00e7ek b\u00f6leni 1 oldu\u011fundan asal say\u0131lar her zaman eksiktir.<\/p>\n<p><strong>Ortak \u00e7arpanlar<\/strong>, iki ya daha fazla say\u0131n\u0131n payla\u015ft\u0131\u011f\u0131 \u00e7arpanlard\u0131r ve tam olarak <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ebob-hesaplama\/\">en b\u00fcy\u00fck ortak b\u00f6lenin (EBOB)<\/a> b\u00f6lenleridir; ara\u00e7 bu y\u00fczden \u00f6nce EBOB'u bulur, sonra b\u00f6lenlerini listeler. Ortak b\u00f6lenler kesirleri sadele\u015ftirmenin anahtar\u0131d\u0131r; bunun e\u015f kavram\u0131 olan en k\u00fc\u00e7\u00fck ortak kat ise <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ekok-hesaplama-en-kucuk-ortak-kat\/\">EKOK Hesaplay\u0131c\u0131s\u0131<\/a>'nda ele al\u0131n\u0131r.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlar ve ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca tam say\u0131lar.<\/strong> Kesirler ve ondal\u0131k say\u0131lar kabul edilmez. S\u0131f\u0131r hari\u00e7 tutulur, \u00e7\u00fcnk\u00fc s\u0131f\u0131rdan farkl\u0131 her tam say\u0131ya tam b\u00f6l\u00fcnd\u00fc\u011f\u00fcnden sonsuz bir liste olu\u015furdu.<\/li>\n<li><strong>B\u00fcy\u00fckl\u00fck s\u0131n\u0131r\u0131.<\/strong> Her say\u0131n\u0131n mutlak de\u011feri en fazla 10\u00b9\u00b2 (1.000.000.000.000.000) olmal\u0131d\u0131r. Binlerce \u00e7arpan\u0131 olan \u00e7ok b\u00fcy\u00fck giri\u015fler k\u0131rp\u0131l\u0131r: listede ilk 2.000 \u00e7arpan, ikili tablosunda en fazla 500 ikili g\u00f6sterilir ve kalan\u0131n say\u0131s\u0131 belirtilir.<\/li>\n<li><strong>Negatif say\u0131lar.<\/strong> Negatif bir de\u011fer girildi\u011finde \\(|n|\\)'in pozitif \u00e7arpanlar\u0131 listelenir ve her birinin \\(-d\\) bi\u00e7iminde bir negatif kar\u015f\u0131l\u0131\u011f\u0131n\u0131n da oldu\u011fu belirtilir; b\u00f6ylece tam say\u0131 \u00e7arpanlar\u0131n toplam say\u0131s\u0131 iki kat\u0131na \u00e7\u0131kar.<\/li>\n<li><strong>\u0130pucu.<\/strong> Bir aday\u0131n \\(n\\)'yi b\u00f6l\u00fcp b\u00f6lmedi\u011fini her \u015feyi listelemeden h\u0131zl\u0131ca denetlemek i\u00e7in \\(n\\)'yi adaya b\u00f6l\u00fcn ve b\u00f6l\u00fcm\u00fcn tam say\u0131 olup olmad\u0131\u011f\u0131na bak\u0131n. Yaln\u0131zca \\(\\sqrt{n}\\)'e kadar olan adaylar\u0131n denenmesi yeterlidir, \u00e7\u00fcnk\u00fc \\(\\sqrt{n}\\)'den b\u00fcy\u00fck her \u00e7arpan, daha \u00f6nce buldu\u011funuz daha k\u00fc\u00e7\u00fck bir \u00e7arpan\u0131n e\u015fidir.<\/li>\n<li><strong>\u0130pucu.<\/strong> \u00c7arpan ikilileri k\u00f6kleri sadele\u015ftirmede ve ikinci dereceden ifadeleri \u00e7arpanlara ay\u0131rmada i\u015fe yarar: \\(a \\times b = n\\) olacak ve \\(a\\) ile \\(b\\)'nin toplam\u0131 ya da fark\u0131 uygun \u00e7\u0131kacak bir ikili bulursan\u0131z, \\(n\\)'in i\u015finize yarayan bir ayr\u0131\u015f\u0131m\u0131n\u0131 bulmu\u015f olursunuz.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>1 ile 10\u00b9\u00b2 aras\u0131nda herhangi bir tam say\u0131 girin; t\u00fcm \u00e7arpanlar\u0131n\u0131, \u00e7arpan (b\u00f6len) say\u0131s\u0131n\u0131 ve toplam\u0131n\u0131, asal \u00e7arpanlara ayr\u0131m\u0131n\u0131, \u00e7arpan ikililerini ve say\u0131n\u0131n asal, m\u00fckemmel, art\u0131kl\u0131 m\u0131 eksik mi oldu\u011funu an\u0131nda g\u00f6r\u00fcn \u2014 ya da 2\u20135 say\u0131y\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131p ortak \u00e7arpanlar\u0131n\u0131 ve EBOB'lar\u0131n\u0131 bulun.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[18],"class_list":["post-4171","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-aritmetik-hesap-makineleri"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4171"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4171\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}