{"id":236713,"date":"2025-06-16T12:40:29","date_gmt":"2025-06-16T12:40:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236713"},"modified":"2025-06-16T12:40:31","modified_gmt":"2025-06-16T12:40:31","slug":"find-the-hcf-by-prime-factorization","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/find-the-hcf-by-prime-factorization\/","title":{"rendered":"Find the HCF by prime factorization."},"content":{"rendered":"\n<p>Find the HCF by prime factorization. 165 and 275 .<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the <strong>Highest Common Factor (HCF)<\/strong> of 165 and 275 using <strong>prime factorization<\/strong>, begin by breaking each number into its prime factors:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime factorization of 165<\/h3>\n\n\n\n<p>165 \u00f7 5 = 33<br>33 \u00f7 3 = 11<br>11 is a prime number.<\/p>\n\n\n\n<p>So, the prime factorization of 165 is:<br><strong>165 = 5 \u00d7 3 \u00d7 11<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Prime factorization of 275<\/h3>\n\n\n\n<p>275 \u00f7 5 = 55<br>55 \u00f7 5 = 11<br>11 is a prime number.<\/p>\n\n\n\n<p>So, the prime factorization of 275 is:<br><strong>275 = 5 \u00d7 5 \u00d7 11<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Identify common prime factors<\/h3>\n\n\n\n<p>Now compare the prime factors of both numbers.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>165 has: 5, 3, 11<\/li>\n\n\n\n<li>275 has: 5, 5, 11<\/li>\n<\/ul>\n\n\n\n<p>The common prime factors are:<br><strong>5 and 11<\/strong><\/p>\n\n\n\n<p>The product of these common factors is:<br><strong>5 \u00d7 11 = 55<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>HCF of 165 and 275 is 55<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words)<\/h3>\n\n\n\n<p>The Highest Common Factor (HCF), also known as the greatest common divisor (GCD), is the largest number that can divide two or more numbers without leaving a remainder. One reliable method to find the HCF is by using <strong>prime factorization<\/strong>, where each number is broken down into a product of its prime numbers.<\/p>\n\n\n\n<p>To begin, consider the number 165. Divide it by the smallest prime number that goes into it, which is 5. Dividing 165 by 5 gives 33. Next, divide 33 by the smallest prime number that fits, which is 3, and the result is 11. Since 11 is already a prime number, the prime factorization of 165 is complete as 5 \u00d7 3 \u00d7 11.<\/p>\n\n\n\n<p>Now move to 275. Dividing 275 by 5 gives 55. Then dividing 55 by 5 again gives 11. Since 11 is a prime number, the prime factorization of 275 is 5 \u00d7 5 \u00d7 11.<\/p>\n\n\n\n<p>Next, compare the two sets of prime factors. Both 165 and 275 have the prime numbers 5 and 11 in common. While 275 has two 5s, 165 has only one. The HCF includes only the prime factors that appear in <strong>both<\/strong> factorizations, taken to the <strong>lowest power<\/strong>. Therefore, take one 5 and one 11.<\/p>\n\n\n\n<p>Multiplying these gives 5 \u00d7 11 = 55. This value is the largest number that can divide both 165 and 275 exactly, with no remainder.<\/p>\n\n\n\n<p>Thus, the HCF of 165 and 275 is 55.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-713.jpeg\" alt=\"\" class=\"wp-image-236714\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the HCF by prime factorization. 165 and 275 . The Correct Answer and Explanation is: To find the Highest Common Factor (HCF) of 165 and 275 using prime factorization, begin by breaking each number into its prime factors: Step 1: Prime factorization of 165 165 \u00f7 5 = 3333 \u00f7 3 = 1111 is [&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-236713","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236713","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=236713"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236713\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236713"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236713"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}