{"id":10339,"date":"2022-04-01T17:14:43","date_gmt":"2022-04-01T11:44:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10339"},"modified":"2022-04-05T18:24:14","modified_gmt":"2022-04-05T12:54:14","slug":"use-euclids-division-algorithm-to-find-the-h-c-f-of","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/use-euclids-division-algorithm-to-find-the-h-c-f-of\/","title":{"rendered":"Use Euclid’s division algorithm to find the H.C.F of :"},"content":{"rendered":"

Question<\/strong> : Use Euclid’s division algorithm to find the H.C.F of :<\/p>\n

(i) 135 and 225<\/p>\n

(ii) 196 and 38220<\/p>\n

(iii) 865 and 225<\/p>\n

Solution<\/strong> :<\/p>\n

(i)<\/strong> We start with the larger number 225.<\/p>\n

By Euclid’s Division Algorithm, we have<\/p>\n

225 = 135 \\(\\times\\) 1 + 90<\/p>\n

We apply Euclid’s Division Algorithm on<\/p>\n

Division 135 and the remainder 90.<\/p>\n

135 = 90 \\(\\times\\) 1 + 45<\/p>\n

Again we apply Euclid’s Division Algorithm on Divisor 90 and remainder 45<\/p>\n

90 = 45 \\(\\times\\) 2 + 0<\/p>\n

H.C.F(225, 90) = 45<\/p>\n

So, H.C.F.\u00a0 of\u00a0 225 and 135 is 45.<\/p>\n

(ii)<\/strong> We have :<\/p>\n

Division = 38200 and Divisor 196<\/p>\n

38220 = 196 \\(\\times\\) 195 + 0<\/p>\n

Hence, H.C.F. (196, 38220) = 196<\/p>\n

(iii)<\/strong> By Euclid’s Division Algorithm, we have<\/p>\n

867 = 255 \\(\\times\\) 3 + 102<\/p>\n

We apply Euclid’s Division Algorithm on the<\/p>\n

Divisor 255 and the remainder 102.<\/p>\n

255 = 102 \\(\\times\\) 2 + 51<\/p>\n

Again we apply Euclid’s Division Algorithm on the divisor 102 and the remainder 51.<\/p>\n

102 = 51 \\(\\times\\) 2 + 0<\/p>\n

H.C.F (867, 255) = H.C.F(255, 102) = H.C.F(102, 51) = 51.<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Use Euclid’s division algorithm to find the H.C.F of : (i) 135 and 225 (ii) 196 and 38220 (iii) 865 and 225 Solution : (i) We start with the larger number 225. By Euclid’s Division Algorithm, we have 225 = 135 \\(\\times\\) 1 + 90 We apply Euclid’s Division Algorithm on Division 135 …<\/p>\n

Use Euclid’s division algorithm to find the H.C.F of :<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,909],"tags":[],"yoast_head":"\nUse Euclid's division algorithm to find the H.C.F of : - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/use-euclids-division-algorithm-to-find-the-h-c-f-of\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Use Euclid's division algorithm to find the H.C.F of : - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question : Use Euclid’s division algorithm to find the H.C.F of : (i) 135 and 225 (ii) 196 and 38220 (iii) 865 and 225 Solution : (i) We start with the larger number 225. 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