{"id":90169,"date":"2025-06-01T10:22:11","date_gmt":"2025-06-01T10:22:11","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90169"},"modified":"2025-06-01T10:22:11","modified_gmt":"2025-06-01T10:22:11","slug":"which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/","title":{"rendered":"Which one of the following is the smallest number by which 2880 must b"},"content":{"rendered":"

Which one of the following is the smallest number by which 2880 must be divided in order to make it a perfect square ?<\/p>\n

[amp_mcq option1=”3″ option2=”4″ option3=”5″ option4=”6″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nTo find the smallest number by which 2880 must be divided to make it a perfect square, we first find the prime factorization of 2880.
\n2880 = 288 * 10 = (144 * 2) * (2 * 5) = (12\u00b2 * 2) * (2 * 5) = ((2\u00b2 * 3)\u00b2) * 2\u00b2 * 5 = (2\u2074 * 3\u00b2) * 2\u00b2 * 5 = 2\u2076 * 3\u00b2 * 5\u00b9
\nFor a number to be a perfect square, the exponents of all its prime factors must be even. In the factorization 2\u2076 * 3\u00b2 * 5\u00b9, the exponents are 6 (even), 2 (even), and 1 (odd).
\nTo make the exponent of 5 even (which is 1), we must divide by 5 raised to the power of its odd exponent, i.e., 5\u00b9.
\nSo, we must divide 2880 by 5.
\n2880 \/ 5 = 576.
\nLet’s check if 576 is a perfect square: 576 = 24 * 24 = 24\u00b2. Yes, it is.
\nTherefore, the smallest number by which 2880 must be divided is 5.
\n<\/section>\n
\nA number is a perfect square if and only if the exponents of all prime factors in its prime factorization are even. To make a number a perfect square by division, divide by the product of prime factors with odd exponents, each raised to the power of their odd exponent.
\n<\/section>\n
\nIf the question asked for the smallest number to *multiply* by, you would multiply by the product of the prime factors with odd exponents, each raised to the power needed to make the exponent even (which is the odd exponent itself). In this case, multiply by 5\u00b9.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following is the smallest number by which 2880 must be divided in order to make it a perfect square ? [amp_mcq option1=”3″ option2=”4″ option3=”5″ option4=”6″ correct=”option3″] This question was previously asked in UPSC CAPF – 2017 Download PDFAttempt Online To find the smallest number by which 2880 must be divided to … <\/p>\n

Detailed SolutionWhich one of the following is the smallest number by which 2880 must b<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1101,1102],"class_list":["post-90169","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1101","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nWhich one of the following is the smallest number by which 2880 must b<\/title>\n<meta name=\"description\" content=\"To find the smallest number by which 2880 must be divided to make it a perfect square, we first find the prime factorization of 2880. 2880 = 288 * 10 = (144 * 2) * (2 * 5) = (12\u00b2 * 2) * (2 * 5) = ((2\u00b2 * 3)\u00b2) * 2\u00b2 * 5 = (2\u2074 * 3\u00b2) * 2\u00b2 * 5 = 2\u2076 * 3\u00b2 * 5\u00b9 For a number to be a perfect square, the exponents of all its prime factors must be even. In the factorization 2\u2076 * 3\u00b2 * 5\u00b9, the exponents are 6 (even), 2 (even), and 1 (odd). To make the exponent of 5 even (which is 1), we must divide by 5 raised to the power of its odd exponent, i.e., 5\u00b9. So, we must divide 2880 by 5. 2880 \/ 5 = 576. Let's check if 576 is a perfect square: 576 = 24 * 24 = 24\u00b2. Yes, it is. Therefore, the smallest number by which 2880 must be divided is 5. A number is a perfect square if and only if the exponents of all prime factors in its prime factorization are even. To make a number a perfect square by division, divide by the product of prime factors with odd exponents, each raised to the power of their odd exponent.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which one of the following is the smallest number by which 2880 must b\" \/>\n<meta property=\"og:description\" content=\"To find the smallest number by which 2880 must be divided to make it a perfect square, we first find the prime factorization of 2880. 2880 = 288 * 10 = (144 * 2) * (2 * 5) = (12\u00b2 * 2) * (2 * 5) = ((2\u00b2 * 3)\u00b2) * 2\u00b2 * 5 = (2\u2074 * 3\u00b2) * 2\u00b2 * 5 = 2\u2076 * 3\u00b2 * 5\u00b9 For a number to be a perfect square, the exponents of all its prime factors must be even. In the factorization 2\u2076 * 3\u00b2 * 5\u00b9, the exponents are 6 (even), 2 (even), and 1 (odd). To make the exponent of 5 even (which is 1), we must divide by 5 raised to the power of its odd exponent, i.e., 5\u00b9. So, we must divide 2880 by 5. 2880 \/ 5 = 576. Let's check if 576 is a perfect square: 576 = 24 * 24 = 24\u00b2. Yes, it is. Therefore, the smallest number by which 2880 must be divided is 5. A number is a perfect square if and only if the exponents of all prime factors in its prime factorization are even. To make a number a perfect square by division, divide by the product of prime factors with odd exponents, each raised to the power of their odd exponent.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:22:11+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Which one of the following is the smallest number by which 2880 must b","description":"To find the smallest number by which 2880 must be divided to make it a perfect square, we first find the prime factorization of 2880. 2880 = 288 * 10 = (144 * 2) * (2 * 5) = (12\u00b2 * 2) * (2 * 5) = ((2\u00b2 * 3)\u00b2) * 2\u00b2 * 5 = (2\u2074 * 3\u00b2) * 2\u00b2 * 5 = 2\u2076 * 3\u00b2 * 5\u00b9 For a number to be a perfect square, the exponents of all its prime factors must be even. In the factorization 2\u2076 * 3\u00b2 * 5\u00b9, the exponents are 6 (even), 2 (even), and 1 (odd). To make the exponent of 5 even (which is 1), we must divide by 5 raised to the power of its odd exponent, i.e., 5\u00b9. So, we must divide 2880 by 5. 2880 \/ 5 = 576. Let's check if 576 is a perfect square: 576 = 24 * 24 = 24\u00b2. Yes, it is. Therefore, the smallest number by which 2880 must be divided is 5. A number is a perfect square if and only if the exponents of all prime factors in its prime factorization are even. To make a number a perfect square by division, divide by the product of prime factors with odd exponents, each raised to the power of their odd exponent.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/","og_locale":"en_US","og_type":"article","og_title":"Which one of the following is the smallest number by which 2880 must b","og_description":"To find the smallest number by which 2880 must be divided to make it a perfect square, we first find the prime factorization of 2880. 2880 = 288 * 10 = (144 * 2) * (2 * 5) = (12\u00b2 * 2) * (2 * 5) = ((2\u00b2 * 3)\u00b2) * 2\u00b2 * 5 = (2\u2074 * 3\u00b2) * 2\u00b2 * 5 = 2\u2076 * 3\u00b2 * 5\u00b9 For a number to be a perfect square, the exponents of all its prime factors must be even. In the factorization 2\u2076 * 3\u00b2 * 5\u00b9, the exponents are 6 (even), 2 (even), and 1 (odd). To make the exponent of 5 even (which is 1), we must divide by 5 raised to the power of its odd exponent, i.e., 5\u00b9. So, we must divide 2880 by 5. 2880 \/ 5 = 576. Let's check if 576 is a perfect square: 576 = 24 * 24 = 24\u00b2. Yes, it is. Therefore, the smallest number by which 2880 must be divided is 5. A number is a perfect square if and only if the exponents of all prime factors in its prime factorization are even. To make a number a perfect square by division, divide by the product of prime factors with odd exponents, each raised to the power of their odd exponent.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:22:11+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/","name":"Which one of the following is the smallest number by which 2880 must b","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:22:11+00:00","dateModified":"2025-06-01T10:22:11+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"To find the smallest number by which 2880 must be divided to make it a perfect square, we first find the prime factorization of 2880. 2880 = 288 * 10 = (144 * 2) * (2 * 5) = (12\u00b2 * 2) * (2 * 5) = ((2\u00b2 * 3)\u00b2) * 2\u00b2 * 5 = (2\u2074 * 3\u00b2) * 2\u00b2 * 5 = 2\u2076 * 3\u00b2 * 5\u00b9 For a number to be a perfect square, the exponents of all its prime factors must be even. In the factorization 2\u2076 * 3\u00b2 * 5\u00b9, the exponents are 6 (even), 2 (even), and 1 (odd). To make the exponent of 5 even (which is 1), we must divide by 5 raised to the power of its odd exponent, i.e., 5\u00b9. So, we must divide 2880 by 5. 2880 \/ 5 = 576. Let's check if 576 is a perfect square: 576 = 24 * 24 = 24\u00b2. Yes, it is. Therefore, the smallest number by which 2880 must be divided is 5. A number is a perfect square if and only if the exponents of all prime factors in its prime factorization are even. To make a number a perfect square by division, divide by the product of prime factors with odd exponents, each raised to the power of their odd exponent.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-smallest-number-by-which-2880-must-b\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"Which one of the following is the smallest number by which 2880 must b"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90169"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90169\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}