{"id":67148,"date":"2026-10-20T09:51:56","date_gmt":"2026-10-20T06:51:56","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67148"},"modified":"2026-10-20T09:51:56","modified_gmt":"2026-10-20T06:51:56","slug":"gcf-calculator-greatest-common-factor","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/gcf-calculator-greatest-common-factor\/","title":{"rendered":"GCF Calculator \u2013 Greatest Common Factor"},"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\">Find the Greatest Common Factor of 2 to 10 Integers<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67148\" data-favorite-title=\"GCF\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/gcf-calculator-greatest-common-factor\/\" data-favorite-excerpt=\"Find the greatest common factor of 2\u201310 integers, along with their least common multiple, prime factorizations, and Euclidean division steps. Enter numbers separated by commas or spaces.\" aria-label=\"Add to Favorites\" 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\/en\/mathematics\/gcf-calculator-greatest-common-factor\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67148\" data-post=\"67148\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Integers<\/label><textarea id=\"field-1\" name=\"integers\">48, 180, 300<\/textarea><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67148\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/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> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Greatest common factor (GCF)<\/span><span class=\"result-term\">GCF<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Least common multiple (LCM)<\/span><span class=\"result-term\">LCM<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Are the numbers coprime?<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Euclidean division steps for the first pair<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Prime factorization of each number<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Common primes at their lowest powers<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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\">Copy link to this calculation<\/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>Leave a Comment<\/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=\"67148\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/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\">Like <\/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\">Helpful <\/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\">Confused <\/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\">Disappointed <\/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\">Inaccurate <\/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>GCF Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[\\operatorname{GCF}(n_1,\\ldots,n_k)=\\prod_{p}p^{\\min\\left(v_p(|n_1|),\\ldots,v_p(|n_k|)\\right)}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(n_1,\\ldots,n_k\\) \u2014 the input integers.<\/li>\n<li>\\(p\\) \u2014 a prime dividing at least one input.<\/li>\n<li>\\(v_p(|n_i|)\\) \u2014 the exponent of \\(p\\) in the prime factorization of \\(|n_i|\\); it is 0 if \\(p\\) does not divide \\(|n_i|\\).<\/li>\n<\/ul>\n<p>The GCF contains only primes shared by every number, each at its lowest exponent. If no prime is shared by all the numbers, the product is 1.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.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>GCF \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the GCF of the calculator\u2019s default integers, 48, 180, and 300.<\/p>\n<p>Factor each number and keep the lowest power of every shared prime:<\/p>\n<p>\\[48=2^4\\times3,\\qquad180=2^2\\times3^2\\times5,\\qquad300=2^2\\times3\\times5^2\\]<\/p>\n<p>\\[\\operatorname{GCF}(48,180,300)=2^{\\min(4,2,2)}\\times3^{\\min(1,2,1)}=2^2\\times3=12\\]<\/p>\n<p>For the first pair, Euclidean division gives \\(180=48\\times3+36\\), \\(48=36\\times1+12\\), and \\(36=12\\times3+0\\). The pair\u2019s GCF is 12; taking the GCF of 12 and 300 leaves 12.<\/p>\n<p><strong>Result:<\/strong> GCF = 12. The calculator also reports LCM = 3,600 and \u201cNo\u201d for coprime.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>In the <strong>Integers<\/strong> field, enter 2\u201310 non-zero integers separated by commas or spaces. For example, enter <code>48, 180, 300<\/code> or <code>48 180 300<\/code>.<\/li>\n<li>Read <strong>Greatest common factor (GCF)<\/strong> for the largest positive integer that divides every entry without a remainder.<\/li>\n<li>Check <strong>Least common multiple (LCM)<\/strong> for the smallest positive multiple shared by every entry. <strong>Are the numbers coprime?<\/strong> says \u201cYes\u201d when their overall GCF is 1.<\/li>\n<li>Use <strong>Euclidean division steps for the first pair<\/strong> to see how the GCF calculation starts. The remaining results show the <strong>Prime factorization of each number<\/strong> and the <strong>Common primes at their lowest powers<\/strong> that produce the final GCF.<\/li>\n<\/ol>\n<h2>What the greatest common factor means<\/h2>\n<p>The greatest common factor, also called the greatest common divisor (GCD), is the largest positive whole number that divides all the given integers exactly. For 48, 180, and 300, that number is 12: each is divisible by 12, and no larger positive integer divides all three. The GCF is useful when simplifying fractions, dividing quantities into equal groups without leftovers, or identifying a common unit of measure.<\/p>\n<p>The prime-factorization method makes the result visible. A prime belongs in the GCF only if it appears in <em>every<\/em> input. Its exponent must be the smallest exponent found among them. In the example, all three numbers contain 2 and 3, while 5 is absent from 48. Keeping \\(2^2\\) and \\(3^1\\) gives 12. To examine one number\u2019s factors in more detail, use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-factorization-calculator\/\">Prime Factorization Calculator<\/a>; the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-number-checker\/\">Prime Number Checker<\/a> can help verify an individual factor.<\/p>\n<p>The Euclidean algorithm reaches the same answer without first finding prime factors. Divide the larger of the first two absolute values by the smaller, then repeat using the divisor and remainder. The last non-zero remainder is that pair\u2019s GCF. For more than two numbers, take the GCF of that result and the next number, continuing through the list. The calculator displays the division steps for the first pair only; its final GCF includes every entry.<\/p>\n<p>An overall GCF of 1 means the numbers are <em>coprime as a group<\/em>. It does not necessarily mean every pair is coprime: 6, 10, and 15 have an overall GCF of 1, although each pair shares a factor. Coprimality is also relevant when working with a <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/multiplicative-inverse-modulo\/\">multiplicative inverse modulo<\/a> a number, where the two integers must have a GCF of 1.<\/p>\n<h2>Input limits and interpretation tips<\/h2>\n<ul>\n<li>Enter at least 2 and at most 10 integers. Zero, decimals, and fractions are not accepted. Each number\u2019s absolute value must be no greater than 1,000,000,000,000.<\/li>\n<li>Negative signs are allowed. The calculator uses absolute values, so changing a number\u2019s sign does not change the GCF or LCM. Both reported values are positive.<\/li>\n<li>The number 1 or \u22121 is allowed and has no prime factors. If it appears among the inputs, the overall GCF is 1.<\/li>\n<li>Do not confuse the GCF with the LCM. The GCF divides every input; the LCM is divisible by every input. Even with the per-input limit, the LCM of several numbers can be much larger than any individual entry.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Find the greatest common factor of 2\u201310 integers, along with their least common multiple, prime factorizations, and Euclidean division steps. Enter numbers separated by commas or spaces.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[72],"class_list":["post-67148","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-arithmetic-calculators"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=67148"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67148\/revisions"}],"predecessor-version":[{"id":67225,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67148\/revisions\/67225"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}