{"id":47409,"date":"2025-07-02T12:00:23","date_gmt":"2025-07-02T12:00:23","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=47409"},"modified":"2025-07-02T12:00:25","modified_gmt":"2025-07-02T12:00:25","slug":"find-the-smallest-number-by-which-576-should-be-divided-to-get-a-perfect-cube","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-smallest-number-by-which-576-should-be-divided-to-get-a-perfect-cube\/","title":{"rendered":"Find the smallest number by which 576 should be divided to get a perfect cube"},"content":{"rendered":"\n<p>Find the smallest number by which 576 should be divided to get a perfect cube.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the smallest number by which 576 should be divided to get a perfect cube, let&#8217;s follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization of 576<\/h3>\n\n\n\n<p>Start by factoring 576 into prime numbers. We can do this through repeated division.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>576 \u00f7 2 = 288<\/li>\n\n\n\n<li>288 \u00f7 2 = 144<\/li>\n\n\n\n<li>144 \u00f7 2 = 72<\/li>\n\n\n\n<li>72 \u00f7 2 = 36<\/li>\n\n\n\n<li>36 \u00f7 2 = 18<\/li>\n\n\n\n<li>18 \u00f7 2 = 9<\/li>\n\n\n\n<li>9 \u00f7 3 = 3<\/li>\n\n\n\n<li>3 \u00f7 3 = 1<\/li>\n<\/ul>\n\n\n\n<p>Thus, the prime factorization of 576 is:<br>576=26\u00d732576 = 2^6 \\times 3^2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify Perfect Cube Conditions<\/h3>\n\n\n\n<p>For a number to be a perfect cube, all the powers of its prime factors must be multiples of 3. Looking at the prime factorization:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>262^6 is not a perfect cube because 6 is not a multiple of 3.<\/li>\n\n\n\n<li>323^2 is not a perfect cube because 2 is not a multiple of 3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Make the Powers of Prime Factors Multiples of 3<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For 262^6, the closest multiple of 3 greater than or equal to 6 is 6 itself, so no adjustment is needed here.<\/li>\n\n\n\n<li>For 323^2, we need to multiply by 313^1 to make the power 3.<\/li>\n<\/ul>\n\n\n\n<p>Thus, to make 576 a perfect cube, we must multiply by 313^1. However, we want the smallest number by which 576 should be divided. So, we need to divide by 323^2 to remove the excess power of 3. Dividing by 32=93^2 = 9 makes the number a perfect cube.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The smallest number by which 576 should be divided to get a perfect cube is <strong>9<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The number 576 has prime factors 262^6 and 323^2. To form a perfect cube, we need to adjust the powers of the prime factors so that each is a multiple of 3. By dividing 576 by 323^2, the power of 3 becomes 0, and the power of 2 is already a multiple of 3. Therefore, the smallest number to divide 576 by to get a perfect cube is 9.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the smallest number by which 576 should be divided to get a perfect cube. The correct answer and explanation is: To find the smallest number by which 576 should be divided to get a perfect cube, let&#8217;s follow these steps: Step 1: Prime Factorization of 576 Start by factoring 576 into prime numbers. We [&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-47409","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47409","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=47409"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47409\/revisions"}],"predecessor-version":[{"id":47414,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47409\/revisions\/47414"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=47409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=47409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=47409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}