What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?<\/p>\n\n\n\n
a) 70<\/p>\n\n\n\n
b) 73<\/strong><\/p>\n\n\n\n c) 77<\/p>\n\n\n\n d) 75<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Given: <\/p>\n\n\n\n Integers 554, 714 and 213 <\/p>\n\n\n\n Concept Used: HCF = Highest Common Factor <\/p>\n\n\n\n Calculation: <\/p>\n\n\n\n \u21d2 According to the question, <\/p>\n\n\n\n \u21d2 If the integer leaves remainder 43, on dividing 554, then it divides 511 exactly <\/p>\n\n\n\n \u21d2 If the integer leaves remainder 57, on dividing 714, then it divides 657 exactly <\/p>\n\n\n\n \u21d2 If the integer leaves remainder 67, on dividing 213, then it divides 146 exactly <\/p>\n\n\n\n \u21d2 On prime factorizing 511, 657 and 146, we have <\/p>\n\n\n\n \u21d2 511 = 7 \u00d7 73 <\/p>\n\n\n\n \u21d2 657 = 3 \u00d7 3 \u00d7 73 <\/p>\n\n\n\n \u21d2 146 = 2 \u00d7 73 <\/p>\n\n\n\n \u21d2 HCF of 511, 657 and 146 = 73 <\/p>\n\n\n\n Therefore, the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively is 73.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively? a) 70 b) 73 c) 77 d) 75 Sol: Given: Integers 554, 714 and 213 Concept Used: HCF = Highest Common Factor Calculation: \u21d2 According to the question, \u21d2 If the integer leaves remainder 43, on […]<\/p>\n","protected":false},"author":419,"featured_media":165514,"comment_status":"open","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-4)","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-4)","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-4)","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":[5138],"tags":[5139],"class_list":["post-165513","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/165513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=165513"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/165513\/revisions"}],"predecessor-version":[{"id":165515,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/165513\/revisions\/165515"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/165514"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=165513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=165513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=165513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}