To find the smallest number by which 375 must be divided to obtain a perfect cube, let’s start by factoring 375 into its prime factors.<\/p>\n\n\n\n
Step 1: Prime Factorization of 375<\/h3>\n\n\n\n
375 can be divided by 5, as it ends in 5.375\u00f75=75375 \\div 5 = 75375\u00f75=75<\/p>\n\n\n\n
Next, divide 75 by 5:75\u00f75=1575 \\div 5 = 1575\u00f75=15<\/p>\n\n\n\n
Finally, divide 15 by 5:15\u00f75=315 \\div 5 = 315\u00f75=3<\/p>\n\n\n\n
So, the prime factorization of 375 is:375=53\u00d73375 = 5^3 \\times 3375=53\u00d73<\/p>\n\n\n\n
Step 2: Identifying What Needs to Be Divided<\/h3>\n\n\n\n
To make 375 a perfect cube, each prime factor’s exponent must be a multiple of 3. In the prime factorization 53\u00d735^3 \\times 353\u00d73, the exponent of 5 is already a multiple of 3 (since 535^353), but the exponent of 3 is 1, which is not a multiple of 3.<\/p>\n\n\n\n
Step 3: Making 375 a Perfect Cube<\/h3>\n\n\n\n
To make 375 a perfect cube, we need to divide by a number that removes the factor of 333 (since it appears to the first power and should be removed for it to be a perfect cube). This means the smallest number we need to divide by is 3.<\/p>\n\n\n\n
Step 4: Final Calculation<\/h3>\n\n\n\n
Now, divide 375 by 3:375\u00f73=125375 \\div 3 = 125375\u00f73=125<\/p>\n\n\n\n
Check if 125 is a perfect cube:125=53125 = 5^3125=53<\/p>\n\n\n\n
Since 125=53125 = 5^3125=53, it is indeed a perfect cube.<\/p>\n\n\n\n
Conclusion<\/h3>\n\n\n\n
The smallest number by which 375 must be divided to obtain a perfect cube is 3<\/strong>.<\/p>\n\n\n\n Find the smallest number by which 375 must be divided to obtain a perfect cube, please. The Correct Answer and Explanation is: To find the smallest number by which 375 must be divided to obtain a perfect cube, let’s start by factoring 375 into its prime factors. Step 1: Prime Factorization of 375 375 can […]<\/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-268198","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268198","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=268198"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268198\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=268198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=268198"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=268198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1760.jpeg\")
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