{"id":28648,"date":"2025-06-20T14:11:21","date_gmt":"2025-06-20T14:11:21","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28648"},"modified":"2025-06-20T14:11:23","modified_gmt":"2025-06-20T14:11:23","slug":"find-the-hcf-of-150-and-225-using-the-prime-factorization-method","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-hcf-of-150-and-225-using-the-prime-factorization-method\/","title":{"rendered":"Find the HCF of 150 and 225 using the prime factorization method"},"content":{"rendered":"\n<p>Find the HCF of 150 and 225 using the prime factorization method. Answer in full definition.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Answer:<\/strong><br>The Highest Common Factor (HCF) of 150 and 225 is <strong>75<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Full Explanation Using Prime Factorization Method:<\/h3>\n\n\n\n<p><strong>Definition:<\/strong><br>The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two or more numbers is the largest number that divides all of them exactly without leaving a remainder.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 1: Prime Factorization of Each Number<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factorization is the process of expressing a number as the product of its prime factors.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the prime factors of <strong>150<\/strong>:<br>150 \u00f7 2 = 75<br>75 \u00f7 3 = 25<br>25 \u00f7 5 = 5<br>5 \u00f7 5 = 1 So, prime factors of 150 are: 150=2\u00d73\u00d75\u00d75=2\u00d73\u00d752150 = 2 \\times 3 \\times 5 \\times 5 = 2 \\times 3 \\times 5^2<\/li>\n\n\n\n<li>Find the prime factors of <strong>225<\/strong>:<br>225 \u00f7 3 = 75<br>75 \u00f7 3 = 25<br>25 \u00f7 5 = 5<br>5 \u00f7 5 = 1 So, prime factors of 225 are: 225=3\u00d73\u00d75\u00d75=32\u00d752225 = 3 \\times 3 \\times 5 \\times 5 = 3^2 \\times 5^2<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 2: Identify the Common Prime Factors<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Look at the prime factors of both numbers:\n<ul class=\"wp-block-list\">\n<li>150 = 2\u00d73\u00d7522 \\times 3 \\times 5^2<\/li>\n\n\n\n<li>225 = 32\u00d7523^2 \\times 5^2<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Common prime factors are those present in <strong>both<\/strong> numbers with the <strong>lowest powers<\/strong>:\n<ul class=\"wp-block-list\">\n<li>For 3: minimum power is 313^1 (because 150 has one 3, and 225 has two 3s)<\/li>\n\n\n\n<li>For 5: minimum power is 525^2 (both have two 5s)<\/li>\n\n\n\n<li>For 2: 225 does not have 2, so exclude it.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 3: Multiply the common factors<\/strong> HCF=31\u00d752=3\u00d725=75HCF = 3^1 \\times 5^2 = 3 \\times 25 = 75<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The HCF is found by prime factorizing both numbers.<\/li>\n\n\n\n<li>Common prime factors with the lowest exponent are multiplied.<\/li>\n\n\n\n<li>For 150 and 225, the HCF is 75.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Why is HCF important?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>HCF is useful in simplifying fractions, finding common denominators, and solving problems involving divisibility.<\/li>\n\n\n\n<li>It represents the greatest number that can evenly divide the given numbers, showing their highest shared factor.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Find the HCF of 150 and 225 using the prime factorization method. Answer in full definition. The correct answer and explanation is: Answer:The Highest Common Factor (HCF) of 150 and 225 is 75. Full Explanation Using Prime Factorization Method: Definition:The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two or [&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-28648","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28648","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=28648"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28648\/revisions"}],"predecessor-version":[{"id":28649,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28648\/revisions\/28649"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}