{"id":67285,"date":"2026-10-21T09:39:56","date_gmt":"2026-10-21T06:39:56","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67285"},"modified":"2026-10-21T09:39:56","modified_gmt":"2026-10-21T06:39:56","slug":"factor-calculator-all-factors-of-a-number","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/factor-calculator-all-factors-of-a-number\/","title":{"rendered":"Factor Calculator \u2013 All Factors of a Number"},"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 Every Factor, Factor Pair and the Prime Factorization<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67285\" data-favorite-title=\"Factors\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/factor-calculator-all-factors-of-a-number\/\" data-favorite-excerpt=\"Enter any whole number up to 10\u00b9\u00b2 and instantly get all of its factors, the number and sum of divisors, the prime factorization, factor pairs, and whether it is prime, perfect, abundant or deficient \u2014 or compare 2\u20135 numbers to find their common factors and GCF.\" 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\/factor-calculator-all-factors-of-a-number\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67285\" data-post=\"67285\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Mode<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"mode\"><option value=\"single\" selected>All factors of one number<\/option><option value=\"common\">Common factors of 2\u20135 numbers<\/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\">Number (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=\"number_n\" id=\"field-2\" aria-describedby=\"calc-info-2\" min=\"-1000000000000\" max=\"1000000000000\" step=\"1\" value=\"360\"\/><small id=\"calc-info-2\">Whole number from 1 to 10\u00b9\u00b2 (10,000,000,000,000). A negative sign is allowed \u2014 the factors of |n| are listed, and the negative factors are noted.<\/small><\/div><div class=\"field is-single\" id=\"input-3\" hidden><label for=\"field-3\">Numbers<\/label><textarea id=\"field-3\" name=\"numbers\">12, 18, 30<\/textarea><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67285\">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 is-column\" id=\"output-1\"><span class=\"field-title\"><span>All factors<\/span><span class=\"result-term\">d<\/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>Number of factors<\/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=\"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>Sum of factors<\/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=\"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>Prime factorization<\/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>Factor pairs (a \u00d7 b = n)<\/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>Prime, perfect, abundant or deficient?<\/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 class=\"field-result is-column\" id=\"output-7\"><span class=\"field-title\"><span>Common factors and GCF<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/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=\"67285\" 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>Factors 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\\[ d \\text{ is a factor of } n \\iff n = d \\cdot k \\text{ for some whole number } k \\]\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>Where:<\/strong><\/p>\n<ul>\n<li>\\(d\\) \u2014 a factor (divisor) of \\(n\\)<\/li>\n<li>\\(n\\) \u2014 the number being factored<\/li>\n<li>\\(p_i\\), \\(e_i\\) \u2014 the distinct prime factors of \\(n\\) and their exponents in the prime factorization<\/li>\n<li>\\(\\tau(n)\\) \u2014 the number of all factors of \\(n\\)<\/li>\n<li>\\(\\sigma(n)\\) \u2014 the sum of all factors of \\(n\\)<\/li>\n<\/ul>\n<p>The first line is the definition of a factor: a number \\(d\\) divides \\(n\\) exactly, with no remainder. The second line shows how the prime factorization determines both how many factors exist and what they add up to.<\/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>Factors \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find all factors of \\(n = 360\\), the calculator's default value.<\/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>Result:<\/strong> 360 has <strong>24 factors<\/strong>: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Their sum is <strong>1170<\/strong>. Since the sum of the proper divisors is \\(1170 - 360 = 810 &gt; 360\\), the number 360 is <strong>abundant<\/strong>. The factors form 12 pairs, from \\(1 \\times 360\\) up to \\(18 \\times 20\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Factor Calculator<\/h2>\n<ol>\n<li>Select the <strong>Mode<\/strong>: <em>All factors of one number<\/em> or <em>Common factors of 2\u20135 numbers<\/em>.<\/li>\n<li>In <em>All factors<\/em> mode, type a whole number from 1 to 10\u00b9\u00b2 into the <strong>Number (n)<\/strong> field. A negative sign is allowed; the calculator lists the factors of \\(|n|\\) and notes the negative ones.<\/li>\n<li>Read the results: <strong>All factors<\/strong> in ascending order, <strong>Number of factors<\/strong> \\(\\tau(n)\\), <strong>Sum of factors<\/strong> \\(\\sigma(n)\\), the <strong>Prime factorization<\/strong>, a table of <strong>Factor pairs<\/strong>, and the classification as prime, perfect, abundant or deficient.<\/li>\n<li>In <em>Common factors<\/em> mode, enter 2\u20135 non-zero whole numbers into the <strong>Numbers<\/strong> box, separated by commas, spaces, semicolons or new lines (for example <code>12, 18, 30<\/code>). The result lists every factor the numbers share, with the <strong>greatest common factor<\/strong> highlighted.<\/li>\n<\/ol>\n<h2>What Factors Are and Why They Matter<\/h2>\n<p>A <strong>factor<\/strong> of a number \\(n\\) is any whole number that divides \\(n\\) without leaving a remainder. For example, 12 is divisible by 1, 2, 3, 4, 6 and 12, so those are all of its factors. Every factor \\(d\\) of \\(n\\) comes with a partner: since \\(n = d \\times k\\), the partner is \\(k = n \\div d\\). That is why factors naturally arrange into <em>factor pairs<\/em>. A number that is a perfect square, such as 36 with the pair \\(6 \\times 6\\), has an odd number of factors because \\(\\sqrt{n}\\) pairs with itself.<\/p>\n<p>The quickest way to find every factor of a large number is the <strong>prime factorization<\/strong>. If \\(n = p_1^{e_1} \\cdot p_2^{e_2} \\cdots p_r^{e_r}\\), every factor is a product of the same primes with exponents no larger than \\(e_i\\). The count follows immediately: \\(\\tau(n) = (e_1+1)(e_2+1)\\cdots(e_r+1)\\). For step-by-step prime decomposition, see the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-factorization-calculator\/\">Prime Factorization Calculator<\/a>; to test a single candidate, the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/prime-number-checker\/\">Prime Number Checker<\/a> is faster.<\/p>\n<p>The sum of factors \\(\\sigma(n)\\) is more than a curiosity \u2014 it classifies the number. If the proper divisors (all factors except \\(n\\) itself) add up to exactly \\(n\\), the number is <strong>perfect<\/strong>, like 6 or 28. If they add up to more, it is <strong>abundant<\/strong>; if less, <strong>deficient<\/strong>. Primes are always deficient, since their only proper divisor is 1.<\/p>\n<p><strong>Common factors<\/strong> are the factors two or more numbers share. They are exactly the factors of the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/gcf-calculator-greatest-common-factor\/\">greatest common factor (GCF)<\/a>, which is why the calculator finds the GCF first and then lists its divisors. Common factors are the key to simplifying fractions; the companion concept, the least common multiple, is covered by the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/lcm-calculator-least-common-multiple\/\">LCM Calculator<\/a>.<\/p>\n<h2>Assumptions, Limits and Tips<\/h2>\n<ul>\n<li><strong>Whole numbers only.<\/strong> Fractions and decimals are rejected. Zero is excluded because it is divisible by every non-zero integer and would produce an infinite list.<\/li>\n<li><strong>Size limit.<\/strong> The absolute value of each number must be at most 10\u00b9\u00b2 (1,000,000,000,000,000). Very large inputs with thousands of factors are truncated: the list shows the first 2,000 factors and the pair table shows up to 500 pairs, with the remainder counted.<\/li>\n<li><strong>Negative numbers.<\/strong> Entering a negative value lists the positive factors of \\(|n|\\) and notes that each also has a negative counterpart \\(-d\\), doubling the total count of integer factors.<\/li>\n<li><strong>Tip.<\/strong> To check quickly whether a candidate divides \\(n\\) without listing everything, divide \\(n\\) by it and see whether the quotient is a whole number. Only candidates up to \\(\\sqrt{n}\\) need testing, because any factor larger than \\(\\sqrt{n}\\) is the partner of a smaller one you already found.<\/li>\n<li><strong>Tip.<\/strong> Factor pairs are handy for simplifying radicals and factoring quadratics: if \\(a \\times b = n\\) with a convenient sum or difference, you have found a useful decomposition of \\(n\\).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Enter any whole number up to 10\u00b9\u00b2 and instantly get all of its factors, the number and sum of divisors, the prime factorization, factor pairs, and whether it is prime, perfect, abundant or deficient \u2014 or compare 2\u20135 numbers to find their common factors and GCF.<\/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-67285","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\/67285","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=67285"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67285\/revisions"}],"predecessor-version":[{"id":67286,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67285\/revisions\/67286"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}