{"id":717,"date":"2025-10-15T10:31:52","date_gmt":"2025-10-15T10:31:52","guid":{"rendered":"https:\/\/kapdec.com\/help\/?post_type=docs&#038;p=717"},"modified":"2026-04-10T10:57:19","modified_gmt":"2026-04-10T10:57:19","slug":"what-is-prime-factorization","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/what-is-prime-factorization\/","title":{"rendered":"What is Prime Factorization?"},"content":{"rendered":"<p><b>Prime Factorization<\/b><\/p>\n<p>&nbsp;<\/p>\n<p>When we express a composite number as a product of prime numbers, it is called\u00a0<b>prime factorization.<\/b>\u00a0The set of prime numbers are called the\u00a0<b>prime factors<\/b>\u00a0of the given number.<\/p>\n<p>&nbsp;<\/p>\n<p><b>Example-<\/b>Let us take a number 24.<\/p>\n<p>Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.<\/p>\n<p>&nbsp;<\/p>\n<p>Out of these factors, the prime factors are 2 and 3.<\/p>\n<p>Now, let us express 24 as a product of its prime factors.<\/p>\n<p>&nbsp;<\/p>\n<p>So, 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3<\/p>\n<p>&nbsp;<\/p>\n<p>Thus,\u00a0<b>prime factorization<\/b>\u00a0is expressing a number as a product of its prime factors.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-720\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/prime-300x106.png\" alt=\"\" width=\"300\" height=\"106\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><b>Method 1:\u00a0Factor Tree Method<\/b><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>In this method, we\u00a0start\u00a0splitting the given numbers into factors until we cannot split anymore.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li>The factor that cannot be split anymore i.e. the prime factor is carried down as it is whereas the composite factor is further split in the next step till it becomes prime.<\/li>\n<li>Then, all the prime factors of the number are stated in product form to define the actual number.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li>The standard way of listing the prime factors is from smallest number to the largest one.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><b>Example\u00a0<\/b>\u2013 Find the prime factorization of 60.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-719\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/example-300x105.png\" alt=\"\" width=\"300\" height=\"105\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Thus, 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5<\/p>\n<p>&nbsp;<\/p>\n<p>#The given number can be treated as a stem while its breakup into prime factors can be treated as its branches.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><b>Method\u00a02:\u00a0Short Division Method<\/b><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>In this method, first we divide the given number by a smallest prime number which completely divides the given number.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li>Then, we divide the quotient again with a smallest prime number or the next smallest prime number which can completely divide the number.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li>We repeat the above step again and again, till the quotient becomes 1.<\/li>\n<\/ul>\n<ul>\n<li>The product of all the divisors that we got through the above step gives us the number itself and are thereby the prime factors of the number.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><b>Example\u00a0<\/b>\u2013 Find the prime factorization of 72.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-718\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/pf-72-252x300.png\" alt=\"\" width=\"252\" height=\"300\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Thus, 72 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Prime Factorization &nbsp; When we express a composite number as a product of prime numbers, it is called\u00a0prime factorization.\u00a0The set of prime numbers are called the\u00a0prime factors\u00a0of the given number. &nbsp; Example-Let us take a number 24. Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24. &nbsp; Out of these factors, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[590],"tags":[595],"class_list":["post-717","post","type-post","status-publish","format-standard","hentry","category-grade-5","tag-grade-5-mathematics"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/717","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=717"}],"version-history":[{"count":1,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/717\/revisions"}],"predecessor-version":[{"id":1563,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/717\/revisions\/1563"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}