{"id":235596,"date":"2025-06-15T14:08:00","date_gmt":"2025-06-15T14:08:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235596"},"modified":"2025-06-15T14:08:02","modified_gmt":"2025-06-15T14:08:02","slug":"find-the-hcf-of-1827-and-54-by-prime-factorisation-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/find-the-hcf-of-1827-and-54-by-prime-factorisation-method\/","title":{"rendered":"find the hcf of 18,27 and 54 by prime factorisation method"},"content":{"rendered":"\n

find the hcf of 18,27 and 54 by prime factorisation method<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong>
The HCF (Highest Common Factor) of 18, 27, and 54 using the prime factorization method is 9<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Step-by-Step Explanation:<\/strong><\/p>\n\n\n\n

1. Prime Factorization of Each Number:<\/strong><\/p>\n\n\n\n

    \n
  • 18 = 2 \u00d7 3 \u00d7 3 = 2 \u00d7 3\u00b2<\/li>\n\n\n\n
  • 27 = 3 \u00d7 3 \u00d7 3 = 3\u00b3<\/li>\n\n\n\n
  • 54 = 2 \u00d7 3 \u00d7 3 \u00d7 3 = 2 \u00d7 3\u00b3<\/li>\n<\/ul>\n\n\n\n

    2. Identify Common Prime Factors:<\/strong><\/p>\n\n\n\n

    All three numbers have at least one common factor: 3<\/strong>.
    The lowest power of 3 in the prime factorization of all three numbers is 3\u00b2<\/strong> (which is 9).
    Even though 2 appears in 18 and 54, it does not appear in 27. So, it is not included in the HCF.<\/p>\n\n\n\n

    3. Multiply the Common Prime Factors:<\/strong><\/p>\n\n\n\n

      \n
    • Only 3\u00b2 is common in all, and no other primes are common.<\/li>\n\n\n\n
    • Therefore, HCF = 3\u00b2 = 9<\/strong><\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Detailed Explanation (300 words):<\/strong><\/p>\n\n\n\n

      The Highest Common Factor (HCF), also known as the greatest common divisor, is the largest positive integer that divides each of the given numbers without leaving a remainder. To determine the HCF of 18, 27, and 54 using the prime factorization method, each number must be broken down into its prime components.<\/p>\n\n\n\n

      Start with 18. Divide by the smallest prime number, 2. Since 18 \u00f7 2 = 9, continue with 9. The number 9 is divisible by 3, giving 3. Dividing again by 3 gives 1. So, 18 = 2 \u00d7 3\u00b2.<\/p>\n\n\n\n

      Now factor 27. It is not divisible by 2 but divisible by 3. Repeated division by 3 yields 27 \u2192 9 \u2192 3 \u2192 1. So, 27 = 3\u00b3.<\/p>\n\n\n\n

      Next, factor 54. Divide by 2 first: 54 \u00f7 2 = 27. Then proceed with 3 repeatedly until reaching 1. The complete factorization is 2 \u00d7 3\u00b3.<\/p>\n\n\n\n

      After listing the prime factors, identify those common to all three numbers. The only prime common to all is 3. The smallest exponent of 3 among the factorizations is 2 (from 18). Therefore, the HCF is obtained by multiplying 3 raised to the smallest power: 3\u00b2 = 9.<\/p>\n\n\n\n

      This method ensures that the largest shared factor is found by considering only the lowest powers of the common prime numbers, resulting in the correct HCF.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      find the hcf of 18,27 and 54 by prime factorisation method The Correct Answer and Explanation is: Correct Answer:The HCF (Highest Common Factor) of 18, 27, and 54 using the prime factorization method is 9. Step-by-Step Explanation: 1. Prime Factorization of Each Number: 2. Identify Common Prime Factors: All three numbers have at least one […]<\/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-235596","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235596","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=235596"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235596\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235596"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235596"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}