{"id":228735,"date":"2025-06-07T13:57:29","date_gmt":"2025-06-07T13:57:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228735"},"modified":"2025-06-07T13:57:31","modified_gmt":"2025-06-07T13:57:31","slug":"find-the-greatest-5-digit-number-that-is-divisible-by-67","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/find-the-greatest-5-digit-number-that-is-divisible-by-67\/","title":{"rendered":"Find the greatest 5 digit number that is divisible by 67"},"content":{"rendered":"\n

Find the greatest 5 digit number that is divisible by 67<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The greatest 5-digit number is 99999<\/strong>. To find the greatest 5-digit number divisible by 67<\/strong>, we divide 99999 by 67 and take the floor<\/strong> (i.e., the greatest whole number less than or equal to the result), then multiply it back by 67:<\/p>\n\n\n\n

Step-by-step:<\/h3>\n\n\n\n

9999967\u22481492.522\\frac{99999}{67} \\approx 1492.5226799999\u200b\u22481492.522<\/p>\n\n\n\n

Taking the floor:\u230a1492.522\u230b=1492\\lfloor 1492.522 \\rfloor = 1492\u230a1492.522\u230b=1492<\/p>\n\n\n\n

Now multiply:1492\u00d767=999641492 \\times 67 = \\boxed{99964}1492\u00d767=99964\u200b<\/p>\n\n\n\n

\n\n\n\n

\u2705 Final Answer: 99964<\/strong><\/h3>\n\n\n\n
\n\n\n\n

\ud83d\udcd8 Explanation<\/h3>\n\n\n\n

To solve this problem, we need to find the greatest 5-digit number<\/strong> that is divisible by 67<\/strong>. A 5-digit number ranges from 10000 to 99999. So, the largest possible 5-digit number is 99999<\/strong>. We are looking for the highest number within this range that can be evenly divided by 67 \u2014 that is, one for which the remainder is zero.<\/p>\n\n\n\n

The method begins with dividing<\/strong> 99999 by 67 to see how many times 67 can fit into it. This division gives a decimal number<\/strong>:99999\u00f767\u22481492.52299999 \\div 67 \\approx 1492.52299999\u00f767\u22481492.522<\/p>\n\n\n\n

This result tells us that 67 can go into 99999 a little over 1492 times. Since we want the greatest whole number of times<\/strong> it goes in without exceeding<\/strong> 99999, we take the floor<\/strong> of this result, which is 1492<\/strong>.<\/p>\n\n\n\n

Next, we multiply:1492\u00d767=999641492 \\times 67 = 999641492\u00d767=99964<\/p>\n\n\n\n

This result, 99964<\/strong>, is a 5-digit number, and importantly, it’s the largest such number<\/strong> divisible by 67.<\/p>\n\n\n\n

If we tried 1493 \u00d7 67, we would get:1493\u00d767=1000311493 \\times 67 = 1000311493\u00d767=100031<\/p>\n\n\n\n

\u2014 which is a 6-digit number<\/strong>, and thus outside the range we want.<\/p>\n\n\n\n

This method is efficient and reliable. By dividing the upper boundary (99999) and using the floor function, we directly pinpoint the highest multiple of 67 within the 5-digit range without checking each number manually.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Find the greatest 5 digit number that is divisible by 67 The Correct Answer and Explanation is: The greatest 5-digit number is 99999. To find the greatest 5-digit number divisible by 67, we divide 99999 by 67 and take the floor (i.e., the greatest whole number less than or equal to the result), then multiply […]<\/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-228735","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228735","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=228735"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228735\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}