{"id":235139,"date":"2025-06-15T02:29:46","date_gmt":"2025-06-15T02:29:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235139"},"modified":"2025-06-15T02:29:48","modified_gmt":"2025-06-15T02:29:48","slug":"find-the-hcf-of-210-140-150-using-prime-factorization-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/find-the-hcf-of-210-140-150-using-prime-factorization-method\/","title":{"rendered":"Find the hcf of 210 140 150 using prime factorization method"},"content":{"rendered":"\n<p>Find the hcf of 210 140 150 using prime factorization method<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the <strong>HCF (Highest Common Factor)<\/strong> of 210, 140, and 150 using the <strong>prime factorization method<\/strong>, follow these steps:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization<\/h3>\n\n\n\n<p><strong>210<\/strong><br>210 \u00f7 2 = 105<br>105 \u00f7 3 = 35<br>35 \u00f7 5 = 7<br>7 \u00f7 7 = 1<br>\u2192 Prime factorization of 210 = <strong>2 \u00d7 3 \u00d7 5 \u00d7 7<\/strong><\/p>\n\n\n\n<p><strong>140<\/strong><br>140 \u00f7 2 = 70<br>70 \u00f7 2 = 35<br>35 \u00f7 5 = 7<br>7 \u00f7 7 = 1<br>\u2192 Prime factorization of 140 = <strong>2\u00b2 \u00d7 5 \u00d7 7<\/strong><\/p>\n\n\n\n<p><strong>150<\/strong><br>150 \u00f7 2 = 75<br>75 \u00f7 3 = 25<br>25 \u00f7 5 = 5<br>5 \u00f7 5 = 1<br>\u2192 Prime factorization of 150 = <strong>2 \u00d7 3 \u00d7 5\u00b2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify Common Prime Factors<\/h3>\n\n\n\n<p>Now list the common prime factors from all three factorizations:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>2<\/strong> is present in all three numbers<\/li>\n\n\n\n<li><strong>5<\/strong> is present in all three numbers<\/li>\n\n\n\n<li><strong>3<\/strong> is not in 140<\/li>\n\n\n\n<li><strong>7<\/strong> is not in 150<\/li>\n<\/ul>\n\n\n\n<p>Thus, the <strong>common prime factors<\/strong> = <strong>2 and 5<\/strong><\/p>\n\n\n\n<p>Now consider the <strong>lowest powers<\/strong> of these common primes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 appears as 2\u00b9 in 210 and 150, and 2\u00b2 in 140 \u2192 take <strong>2\u00b9<\/strong><\/li>\n\n\n\n<li>5 appears as 5\u00b9 in 210 and 140, and 5\u00b2 in 150 \u2192 take <strong>5\u00b9<\/strong><\/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\">Step 3: Multiply the Common Prime Factors<\/h3>\n\n\n\n<p>HCF = 2\u00b9 \u00d7 5\u00b9 = <strong>2 \u00d7 5 = 10<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer: <strong>10<\/strong><\/h3>\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 Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), represents the largest positive number that divides all the given numbers without leaving a remainder. The prime factorization method is a systematic approach to identify this number.<\/p>\n\n\n\n<p>To apply this method, each number must first be broken down into its prime components. Prime numbers are numbers greater than 1 that are divisible only by 1 and themselves. By repeatedly dividing the number by the smallest possible prime numbers, a product of primes is obtained. This process continues until the result is 1.<\/p>\n\n\n\n<p>Once all numbers are factorized, the next step is to examine the prime factors of each and identify the common ones. It is important to only consider the prime numbers that appear in all the factorizations. The HCF is then determined by multiplying these common primes using their smallest powers found in the individual factorizations.<\/p>\n\n\n\n<p>For the numbers 210, 140, and 150, the prime factorizations are 2 \u00d7 3 \u00d7 5 \u00d7 7, 2\u00b2 \u00d7 5 \u00d7 7, and 2 \u00d7 3 \u00d7 5\u00b2 respectively. The only primes that appear in all three are 2 and 5. Among these, the lowest power of 2 is 2\u00b9 and the lowest power of 5 is 5\u00b9. Multiplying them results in 2 \u00d7 5 = 10, which is the largest number that divides all three numbers exactly.<\/p>\n\n\n\n<p>This method is especially useful for large numbers and ensures that no common factor is missed. It also helps reinforce an understanding of prime numbers and their role in number theory.<\/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-banner5-544.jpeg\" alt=\"\" class=\"wp-image-235140\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the hcf of 210 140 150 using prime factorization method The Correct Answer and Explanation is: To find the HCF (Highest Common Factor) of 210, 140, and 150 using the prime factorization method, follow these steps: Step 1: Prime Factorization 210210 \u00f7 2 = 105105 \u00f7 3 = 3535 \u00f7 5 = 77 \u00f7 [&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-235139","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235139","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=235139"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235139\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235139"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235139"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}