{"id":25538,"date":"2025-06-19T03:42:44","date_gmt":"2025-06-19T03:42:44","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25538"},"modified":"2025-06-19T03:42:46","modified_gmt":"2025-06-19T03:42:46","slug":"find-the-hcf-of-the-following-numbers-by-prime-factorization-method","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-hcf-of-the-following-numbers-by-prime-factorization-method\/","title":{"rendered":"Find the HCF of the following numbers by prime factorization method."},"content":{"rendered":"\n<p>Find the HCF of the following numbers by prime factorization method. (a) 76, 28 (b) 24, 16, 36 (c) 38, 64, 82<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s find the <strong>HCF (Highest Common Factor)<\/strong> of the given numbers using the <strong>prime factorization method<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(a) <strong>76 and 28<\/strong><\/h3>\n\n\n\n<p><strong>Prime factorization:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>76 = 2 \u00d7 2 \u00d7 19 = 2\u00b2 \u00d7 19<\/li>\n\n\n\n<li>28 = 2 \u00d7 2 \u00d7 7 = 2\u00b2 \u00d7 7<\/li>\n<\/ul>\n\n\n\n<p><strong>Common prime factors<\/strong>: 2\u00b2<br>So, <strong>HCF = 2\u00b2 = 4<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(b) <strong>24, 16, and 36<\/strong><\/h3>\n\n\n\n<p><strong>Prime factorizations:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 = 2\u00b3 \u00d7 3<\/li>\n\n\n\n<li>16 = 2 \u00d7 2 \u00d7 2 \u00d7 2 = 2\u2074<\/li>\n\n\n\n<li>36 = 2 \u00d7 2 \u00d7 3 \u00d7 3 = 2\u00b2 \u00d7 3\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>Common prime factor<\/strong>: 2 (only base 2 is common in all)<br>Take the <strong>lowest exponent<\/strong> of 2, which is 2\u00b9<\/p>\n\n\n\n<p>So, <strong>HCF = 2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(c) <strong>38, 64, and 82<\/strong><\/h3>\n\n\n\n<p><strong>Prime factorizations:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>38 = 2 \u00d7 19<\/li>\n\n\n\n<li>64 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 2\u2076<\/li>\n\n\n\n<li>82 = 2 \u00d7 41<\/li>\n<\/ul>\n\n\n\n<p><strong>Common prime factor<\/strong>: 2 (only 2 appears in all three)<br>Lowest exponent of 2 is 2\u00b9<\/p>\n\n\n\n<p>So, <strong>HCF = 2<\/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:<\/h3>\n\n\n\n<p>The <strong>Highest Common Factor (HCF)<\/strong> is the greatest number that divides all the given numbers exactly. One of the most reliable ways to find the HCF is by using <strong>prime factorization<\/strong>, where we express each number as a product of its prime numbers.<\/p>\n\n\n\n<p>To start, we break down each number into its prime factors. Then, we identify which prime factors are <strong>common to all numbers<\/strong> in the set. After that, we select the <strong>lowest power (exponent)<\/strong> of each common prime factor. Finally, we multiply these lowest powers together to find the HCF.<\/p>\n\n\n\n<p>Let us apply this step by step:<\/p>\n\n\n\n<p>In part (a), both 76 and 28 have the prime number 2 as a common factor. Since the highest power of 2 common to both is 2\u00b2, the HCF is 4.<\/p>\n\n\n\n<p>In part (b), 24, 16, and 36 all contain the prime number 2, but with different powers. 24 has 2\u00b3, 16 has 2\u2074, and 36 has 2\u00b2. The smallest power is 2\u00b9, so HCF is 2. Other prime factors such as 3 are not common to all three numbers, so we ignore them.<\/p>\n\n\n\n<p>In part (c), although the numbers are quite different, all have 2 as a common prime factor. Even though 64 has many twos, we only take the lowest common count, which is 1, giving an HCF of 2.<\/p>\n\n\n\n<p>This method is systematic, reduces error, and helps with large numbers<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-50.jpeg\" alt=\"\" class=\"wp-image-25539\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-50.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-50-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-50-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n\n\n\n<p>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the HCF of the following numbers by prime factorization method. (a) 76, 28 (b) 24, 16, 36 (c) 38, 64, 82 The Correct Answer and Explanation is: Let&#8217;s find the HCF (Highest Common Factor) of the given numbers using the prime factorization method. (a) 76 and 28 Prime factorization: Common prime factors: 2\u00b2So, HCF [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-25538","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25538","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=25538"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25538\/revisions"}],"predecessor-version":[{"id":25540,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25538\/revisions\/25540"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}