Write 1260, 2535 and 15625 as a product of prime factors.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To express the numbers 1260, 2535, and 15625 as a product of prime factors, we need to perform prime factorization on each number. Prime factorization involves dividing the number by prime numbers (2, 3, 5, 7, 11, etc.) until we can no longer divide evenly by any prime number.<\/p>\n\n\n\n Start by dividing 1260 by the smallest prime number, 2, since 1260 is even.<\/p>\n\n\n\n 1260 \u00f7 2 = 630<\/p>\n\n\n\n Now, divide 630 by 2 again:<\/p>\n\n\n\n 630 \u00f7 2 = 315<\/p>\n\n\n\n Next, divide 315 by the next smallest prime, 3:<\/p>\n\n\n\n 315 \u00f7 3 = 105<\/p>\n\n\n\n Divide 105 by 3 again:<\/p>\n\n\n\n 105 \u00f7 3 = 35<\/p>\n\n\n\n Now divide 35 by the next smallest prime, 5:<\/p>\n\n\n\n 35 \u00f7 5 = 7<\/p>\n\n\n\n Finally, 7 is already a prime number.<\/p>\n\n\n\n Thus, the prime factorization of 1260 is:<\/p>\n\n\n\n 1260 = 2\u00b2 \u00d7 3\u00b2 \u00d7 5 \u00d7 7<\/p>\n\n\n\n Start by dividing 2535 by 3 (since the sum of digits of 2535 is divisible by 3):<\/p>\n\n\n\n 2535 \u00f7 3 = 845<\/p>\n\n\n\n Now divide 845 by 5 (since it ends in 5):<\/p>\n\n\n\n 845 \u00f7 5 = 169<\/p>\n\n\n\n Finally, 169 is a perfect square, and its square root is 13, which is prime:<\/p>\n\n\n\n 169 \u00f7 13 = 13<\/p>\n\n\n\n Thus, the prime factorization of 2535 is:<\/p>\n\n\n\n 2535 = 3 \u00d7 5 \u00d7 13\u00b2<\/p>\n\n\n\n 15625 is not divisible by 2, 3, or 5, so we check divisibility by higher primes. It turns out that 15625 is a power of 5:<\/p>\n\n\n\n 15625 \u00f7 5 = 3125<\/p>\n\n\n\n 3125 \u00f7 5 = 625<\/p>\n\n\n\n 625 \u00f7 5 = 125<\/p>\n\n\n\n 125 \u00f7 5 = 25<\/p>\n\n\n\n 25 \u00f7 5 = 5<\/p>\n\n\n\n 5 \u00f7 5 = 1<\/p>\n\n\n\n Thus, the prime factorization of 15625 is:<\/p>\n\n\n\n 15625 = 5\u2076<\/p>\n\n\n\n Prime factorization breaks each number down into the prime numbers that multiply to give the original number. This method helps in simplifying calculations, such as finding the greatest common divisor or the least common multiple.<\/p>\n","protected":false},"excerpt":{"rendered":" Write 1260, 2535 and 15625 as a product of prime factors. The correct answer and explanation is: To express the numbers 1260, 2535, and 15625 as a product of prime factors, we need to perform prime factorization on each number. Prime factorization involves dividing the number by prime numbers (2, 3, 5, 7, 11, etc.) […]<\/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-246515","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246515","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=246515"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246515\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246515"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246515"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}1. Prime Factorization of 1260:<\/h3>\n\n\n\n
2. Prime Factorization of 2535:<\/h3>\n\n\n\n
3. Prime Factorization of 15625:<\/h3>\n\n\n\n
Summary:<\/h3>\n\n\n\n
\n