{"id":246361,"date":"2025-07-07T06:49:44","date_gmt":"2025-07-07T06:49:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246361"},"modified":"2025-07-07T06:49:47","modified_gmt":"2025-07-07T06:49:47","slug":"137-divided-by-4-equals-34-with-a-remainder-of-1-34-divided-by-4-equals-8-with-a-remainder-of-2-8-divided-by-4-equals-2-with-a-remainder-of-0-2-divided-by-4-equals-0-with-a-remainder-of-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/137-divided-by-4-equals-34-with-a-remainder-of-1-34-divided-by-4-equals-8-with-a-remainder-of-2-8-divided-by-4-equals-2-with-a-remainder-of-0-2-divided-by-4-equals-0-with-a-remainder-of-2\/","title":{"rendered":"137 divided by 4 equals 34 with a remainder of 1. 34 divided by 4 equals 8 with a remainder of 2. 8 divided by 4 equals 2 with a remainder of 0. 2 divided by 4 equals 0 with a remainder of 2."},"content":{"rendered":"\n

137 divided by 4 equals 34 with a remainder of 1. 34 divided by 4 equals 8 with a remainder of 2. 8 divided by 4 equals 2 with a remainder of 0. 2 divided by 4 equals 0 with a remainder of 2. Therefore, the base-4 representation of 137 is 2201_4. The remainders are whole numbers because when dividing, the quotient represents the number of times the divisor can be subtracted from the dividend, and the remainder represents what is left over. To obtain the base-4 representation, we start from the last remainder and work our way up. Each remainder represents a digit in the base-4 number system. In this case, the remainders are 1, 2, 0, and 2, which correspond to the digits 1, 2, 0, and 2 in base-4. Therefore, the base-4 representation of 137 is 2201_4.<\/p>\n\n\n\n

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

Step-by-Step Conversion:<\/h3>\n\n\n\n
    \n
  1. Start with 137 and divide by 4.<\/strong>
    137\u00f74=34137 \\div 4 = 34137\u00f74=34 with a remainder of 1.
    This means 137 can be written as:
    137=4\u00d734+1137 = 4 \\times 34 + 1137=4\u00d734+1.
    The remainder, 1, is the least significant digit (rightmost) in the base-4 number.<\/li>\n\n\n\n
  2. Next, divide 34 by 4.<\/strong>
    34\u00f74=834 \\div 4 = 834\u00f74=8 with a remainder of 2.
    This gives:
    34=4\u00d78+234 = 4 \\times 8 + 234=4\u00d78+2.
    The remainder, 2, is the next digit in the base-4 representation.<\/li>\n\n\n\n
  3. Then, divide 8 by 4.<\/strong>
    8\u00f74=28 \\div 4 = 28\u00f74=2 with a remainder of 0.
    This gives:
    8=4\u00d72+08 = 4 \\times 2 + 08=4\u00d72+0.
    The remainder, 0, is the next digit in the base-4 representation.<\/li>\n\n\n\n
  4. Finally, divide 2 by 4.<\/strong>
    2\u00f74=02 \\div 4 = 02\u00f74=0 with a remainder of 2.
    This gives:
    2=4\u00d70+22 = 4 \\times 0 + 22=4\u00d70+2.
    The remainder, 2, is the most significant digit (leftmost) in the base-4 number.<\/li>\n<\/ol>\n\n\n\n

    Reading the remainders from last to first, the base-4 representation of 137 is 2021\u2084<\/strong>.<\/h3>\n\n\n\n

    Why This Works:<\/h3>\n\n\n\n

    In this method, each remainder gives us one digit of the number in the new base, and we read the remainders from last to first because the division process starts from the least significant digit (rightmost) to the most significant (leftmost). The base-4 system uses digits from 0 to 3, so the remainders 1, 2, 0, and 2 correspond directly to the digits of the base-4 number.<\/p>\n\n\n\n

    Thus, the correct base-4 representation of 137 is 2021\u2084<\/strong>.<\/p>\n\n\n\n

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

    137 divided by 4 equals 34 with a remainder of 1. 34 divided by 4 equals 8 with a remainder of 2. 8 divided by 4 equals 2 with a remainder of 0. 2 divided by 4 equals 0 with a remainder of 2. Therefore, the base-4 representation of 137 is 2201_4. The remainders are […]<\/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-246361","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246361","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=246361"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246361\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246361"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246361"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246361"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}