{"id":156592,"date":"2024-10-17T12:06:27","date_gmt":"2024-10-17T12:06:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156592"},"modified":"2024-10-17T12:06:29","modified_gmt":"2024-10-17T12:06:29","slug":"360-is-divisible-by-which-of-the-following-numbers-234569-or-10","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/360-is-divisible-by-which-of-the-following-numbers-234569-or-10\/","title":{"rendered":"360 is divisible by which of the following numbers 2,3,4,5,6,9, or 10"},"content":{"rendered":"\n

360 is divisible by which of the following numbers 2,3,4,5,6,9, or 10<\/p>\n\n\n\n

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

To determine which of the numbers 2, 3, 4, 5, 6, 9, and 10 are divisors of 360, we need to perform a divisibility test for each number.<\/p>\n\n\n\n

Step 1: Prime Factorization of 360<\/h3>\n\n\n\n

First, let’s find the prime factorization of 360 to help us understand its divisibility:<\/p>\n\n\n\n

    \n
  1. Start by dividing by the smallest prime number, 2:<\/li>\n<\/ol>\n\n\n\n
      \n
    • (360 \\div 2 = 180)<\/li>\n\n\n\n
    • (180 \\div 2 = 90)<\/li>\n\n\n\n
    • (90 \\div 2 = 45)<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Next, we divide by the next smallest prime, which is 3:<\/li>\n<\/ol>\n\n\n\n
          \n
        • (45 \\div 3 = 15)<\/li>\n\n\n\n
        • (15 \\div 3 = 5)<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Finally, we are left with the prime number 5:<\/li>\n<\/ol>\n\n\n\n
              \n
            • (5 \\div 5 = 1)<\/li>\n<\/ul>\n\n\n\n

              Thus, the prime factorization of 360 is:
              [ 360 = 2^3 \\times 3^2 \\times 5^1 ]<\/p>\n\n\n\n

              Step 2: Divisibility Tests<\/h3>\n\n\n\n

              Now, we can check each number for divisibility based on the factorization:<\/p>\n\n\n\n

                \n
              1. 2<\/strong>: Since 360 includes (2^3), it is divisible by 2.<\/li>\n\n\n\n
              2. 3<\/strong>: The factorization includes (3^2), so 360 is divisible by 3.<\/li>\n\n\n\n
              3. 4<\/strong>: 4 can be expressed as (2^2). Since 360 includes (2^3), it is divisible by 4.<\/li>\n\n\n\n
              4. 5<\/strong>: The factorization includes (5^1), so 360 is divisible by 5.<\/li>\n\n\n\n
              5. 6<\/strong>: Since 6 is the product of 2 and 3, and both factors are present in the factorization, 360 is divisible by 6.<\/li>\n\n\n\n
              6. 9<\/strong>: 9 is (3^2), and since 360 includes (3^2), it is divisible by 9.<\/li>\n\n\n\n
              7. 10<\/strong>: 10 is the product of 2 and 5, both of which are present, so 360 is divisible by 10.<\/li>\n<\/ol>\n\n\n\n

                Conclusion<\/h3>\n\n\n\n

                In summary, 360 is divisible by all<\/strong> of the following numbers: 2, 3, 4, 5, 6, 9, and 10<\/strong>. This shows the importance of understanding prime factorization, as it simplifies the process of determining divisibility by breaking down the numbers into their fundamental components.<\/p>\n","protected":false},"excerpt":{"rendered":"

                360 is divisible by which of the following numbers 2,3,4,5,6,9, or 10 The Correct Answer and Explanation is : To determine which of the numbers 2, 3, 4, 5, 6, 9, and 10 are divisors of 360, we need to perform a divisibility test for each number. Step 1: Prime Factorization of 360 First, let’s […]<\/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-156592","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156592","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=156592"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156592\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}