{"id":241367,"date":"2025-07-03T17:10:58","date_gmt":"2025-07-03T17:10:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241367"},"modified":"2025-07-03T17:10:59","modified_gmt":"2025-07-03T17:10:59","slug":"1234567-99-is-divide-by-99-than-reminder-then-find-reminder-is","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/1234567-99-is-divide-by-99-than-reminder-then-find-reminder-is\/","title":{"rendered":"1234567\u2026.99 is divide by 99 than reminder then find reminder is"},"content":{"rendered":"\n

1234567\u2026.99 is divide by 99 than reminder then find reminder is<\/p>\n\n\n\n

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

To find the remainder when dividing a number that consists of digits from 1 to 99 (i.e., the number 1234567…99) by 99, we can break this down into simpler steps. The number is a large sequence, but there is a helpful property we can use: the remainder of a number when divided by 99 depends only on the sum of its digits.<\/p>\n\n\n\n

Steps:<\/h3>\n\n\n\n
    \n
  1. Sum the digits of the number<\/strong>:
    The number consists of all integers from 1 to 99 written in sequence, so the digits involved are from 1 to 99. To find the sum of all the digits in the number, we can break it into parts:
    • The digits from 1 to 9 sum to 1+2+3+4+5+6+7+8+9=451 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 451+2+3+4+5+6+7+8+9=45.<\/li>
    • The digits from 10 to 99 require summing each of their tens and ones digits.<\/li><\/ul>For the tens digits (10, 20, …, 90), the sum is:
      1+2+3+4+5+6+7+8+9=451 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 451+2+3+4+5+6+7+8+9=45.
      These tens digits appear 10 times each (i.e., 10, 20, …, 90), so the total for the tens digits is 45\u00d710=45045 \\times 10 = 45045\u00d710=450. For the ones digits, each appears exactly 9 times, so their sum is:
      (1+2+3+…+9)\u00d79=45\u00d79=405(1 + 2 + 3 + … + 9) \\times 9 = 45 \\times 9 = 405(1+2+3+…+9)\u00d79=45\u00d79=405. Therefore, the total sum of all digits is:
      45+450+405=90045 + 450 + 405 = 90045+450+405=900.<\/li>\n\n\n\n
    • Find the remainder when the sum is divided by 99<\/strong>:
      Now, we simply divide the sum of the digits (900) by 99 to find the remainder:
      900\u00f799=9\u00a0remainder\u00a09900 \\div 99 = 9 \\text{ remainder } 9900\u00f799=9\u00a0remainder\u00a09.<\/li>\n<\/ol>\n\n\n\n

      Thus, the remainder when the number 123456789101112…99 is divided by 99 is 9<\/strong>.<\/p>\n\n\n\n

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

      1234567\u2026.99 is divide by 99 than reminder then find reminder is The Correct Answer and Explanation is: To find the remainder when dividing a number that consists of digits from 1 to 99 (i.e., the number 1234567…99) by 99, we can break this down into simpler steps. The number is a large sequence, but there […]<\/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-241367","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241367","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=241367"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241367\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}