{"id":259661,"date":"2025-07-19T04:51:54","date_gmt":"2025-07-19T04:51:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259661"},"modified":"2025-07-19T04:51:57","modified_gmt":"2025-07-19T04:51:57","slug":"find-the-hcf-of-45-60-and-72-using-prime-factorization","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/19\/find-the-hcf-of-45-60-and-72-using-prime-factorization\/","title":{"rendered":"Find the HCF of 45 , 60 and 72 using prime factorization&#8221;"},"content":{"rendered":"\n<p>Find the HCF of 45 , 60 and 72 using prime factorization&#8221;<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the Highest Common Factor (HCF) of 45, 60, and 72 using prime factorization, follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the prime factorization of each number.<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Prime factorization of 45:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing 45 by 3 (the smallest prime number):\n<ul class=\"wp-block-list\">\n<li>45 \u00f7 3 = 15<\/li>\n\n\n\n<li>15 \u00f7 3 = 5<\/li>\n\n\n\n<li>5 \u00f7 5 = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Prime factorization of 45: $45 = 3^2 \\times 5$<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Prime factorization of 60:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing 60 by 2 (the smallest prime number):\n<ul class=\"wp-block-list\">\n<li>60 \u00f7 2 = 30<\/li>\n\n\n\n<li>30 \u00f7 2 = 15<\/li>\n\n\n\n<li>15 \u00f7 3 = 5<\/li>\n\n\n\n<li>5 \u00f7 5 = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Prime factorization of 60: $60 = 2^2 \\times 3 \\times 5$<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Prime factorization of 72:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start by dividing 72 by 2 (the smallest prime number):\n<ul class=\"wp-block-list\">\n<li>72 \u00f7 2 = 36<\/li>\n\n\n\n<li>36 \u00f7 2 = 18<\/li>\n\n\n\n<li>18 \u00f7 2 = 9<\/li>\n\n\n\n<li>9 \u00f7 3 = 3<\/li>\n\n\n\n<li>3 \u00f7 3 = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Prime factorization of 72: $72 = 2^3 \\times 3^2$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the common prime factors.<\/h3>\n\n\n\n<p>Now, compare the prime factorizations of all three numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$45 = 3^2 \\times 5$<\/li>\n\n\n\n<li>$60 = 2^2 \\times 3 \\times 5$<\/li>\n\n\n\n<li>$72 = 2^3 \\times 3^2$<\/li>\n<\/ul>\n\n\n\n<p>The only common prime factor between all three numbers is <strong>3<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Choose the lowest power of the common prime factors.<\/h3>\n\n\n\n<p>For 3, the lowest power is $3^1$, because it appears as $3^1$ in 60 and $3^2$ in both 45 and 72.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Calculate the HCF.<\/h3>\n\n\n\n<p>Since 3 is the only common prime factor, the HCF of 45, 60, and 72 is $3^1 = 3$.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The HCF of 45, 60, and 72 is <strong>3<\/strong>. This method ensures that we only consider the prime factors common to all three numbers and select the smallest power for each prime factor to get the highest common divisor.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the HCF of 45 , 60 and 72 using prime factorization&#8221; The correct answer and explanation is: To find the Highest Common Factor (HCF) of 45, 60, and 72 using prime factorization, follow these steps: Step 1: Find the prime factorization of each number. Step 2: Find the common prime factors. Now, compare the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-259661","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259661","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=259661"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259661\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}