{"id":232908,"date":"2025-06-12T11:11:07","date_gmt":"2025-06-12T11:11:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232908"},"modified":"2025-06-12T11:11:09","modified_gmt":"2025-06-12T11:11:09","slug":"remainder","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/remainder\/","title":{"rendered":"Remainder."},"content":{"rendered":"\n<p>Remainder. Find the greatest number that divides 48 and 76 with 6 as remainder in both cases<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>The greatest number that divides <strong>48<\/strong> and <strong>76<\/strong>, leaving a remainder of <strong>6<\/strong> in both cases, is <strong>14<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>To solve this problem, we are given that the same number leaves a remainder of <strong>6<\/strong> when it divides both <strong>48<\/strong> and <strong>76<\/strong>. Our goal is to find the <strong>greatest number<\/strong> that satisfies this condition.<\/p>\n\n\n\n<p>Let us understand what this means mathematically.<\/p>\n\n\n\n<p>If a number <strong>d<\/strong> divides <strong>48<\/strong> and leaves a remainder <strong>6<\/strong>, then:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>48 = d \u00d7 q\u2081 + 6<br>\u21d2 48 \u2212 6 = d \u00d7 q\u2081<br>\u21d2 42 is divisible by d<\/p>\n<\/blockquote>\n\n\n\n<p>Similarly, if the same number <strong>d<\/strong> divides <strong>76<\/strong> and leaves a remainder <strong>6<\/strong>, then:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>76 = d \u00d7 q\u2082 + 6<br>\u21d2 76 \u2212 6 = d \u00d7 q\u2082<br>\u21d2 70 is divisible by d<\/p>\n<\/blockquote>\n\n\n\n<p>This tells us that the number <strong>d<\/strong> divides both <strong>42<\/strong> and <strong>70<\/strong> exactly. Therefore, <strong>d<\/strong> must be a common divisor of <strong>42<\/strong> and <strong>70<\/strong>.<\/p>\n\n\n\n<p>Now, to find the <strong>greatest number<\/strong> that satisfies this condition, we must compute the <strong>greatest common divisor (GCD)<\/strong> of 42 and 70.<\/p>\n\n\n\n<p>Let\u2019s list the factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42<\/li>\n\n\n\n<li>Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70<\/li>\n<\/ul>\n\n\n\n<p>Common factors of 42 and 70 are: <strong>1, 2, 7, 14<\/strong><\/p>\n\n\n\n<p>The <strong>greatest<\/strong> of these is <strong>14<\/strong>.<\/p>\n\n\n\n<p>Hence, the greatest number that divides both <strong>48<\/strong> and <strong>76<\/strong>, leaving a remainder of <strong>6<\/strong> in each case, is <strong>14<\/strong>.<\/p>\n\n\n\n<p><strong>Verification:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>48 \u00f7 14 = 3 remainder <strong>6<\/strong> \u2705<\/li>\n\n\n\n<li>76 \u00f7 14 = 5 remainder <strong>6<\/strong> \u2705<\/li>\n<\/ul>\n\n\n\n<p>This confirms that 14 is the correct answer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-371.jpeg\" alt=\"\" class=\"wp-image-232909\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Remainder. Find the greatest number that divides 48 and 76 with 6 as remainder in both cases The Correct Answer and Explanation is: Correct Answer:The greatest number that divides 48 and 76, leaving a remainder of 6 in both cases, is 14. Explanation To solve this problem, we are given that the same number leaves [&hellip;]<\/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-232908","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232908","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=232908"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232908\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}