{"id":223008,"date":"2025-06-01T07:10:33","date_gmt":"2025-06-01T07:10:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223008"},"modified":"2025-06-01T07:10:35","modified_gmt":"2025-06-01T07:10:35","slug":"4-b-is-67-108-divisible-by-8-give-a-reason-for-your-answer","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/4-b-is-67-108-divisible-by-8-give-a-reason-for-your-answer\/","title":{"rendered":"4 b Is 67 108 divisible by 8? Give a reason for your answer."},"content":{"rendered":"\n<p>4 b Is 67 108 divisible by 8? Give a reason for your answer. no 67108 cannot be divisible The number 3812* is divisible by 3. The final digit is missing. What can you say about the missing digit?<br>4 b Is 67 108 divisible by 8? Give a reason for your answer. no 67108 cannot be divisible The number 3812* is divisible by 3. The final digit is missing. What can you say about the missing digit?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s answer both parts of the question correctly and explain them in detail:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Question 1: Is 67,108 divisible by 8?<\/strong><\/p>\n\n\n\n<p><strong>Answer:<\/strong><br><strong>Yes, 67,108 is divisible by 8.<\/strong><\/p>\n\n\n\n<p><strong>Reason:<\/strong><br>To check if a number is divisible by 8, we look at its last <strong>three digits<\/strong>. If the last three digits form a number that is divisible by 8, then the whole number is divisible by 8.<\/p>\n\n\n\n<p>In <strong>67,108<\/strong>, the last three digits are <strong>108<\/strong>.<br>Now check if <strong>108 \u00f7 8 = 13.5<\/strong> \u2014 This is <strong>not<\/strong> a whole number, so 108 is <strong>not divisible<\/strong> by 8.<\/p>\n\n\n\n<p>Thus, <strong>67,108 is NOT divisible by 8.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><em>Question 2: The number 3812 is divisible by 3. The final digit is missing. What can you say about the missing digit?<\/em>*<\/p>\n\n\n\n<p><strong>Answer:<\/strong><br>To determine the missing digit, we use the <strong>rule of divisibility for 3<\/strong>:<br>A number is divisible by 3 if the <strong>sum of its digits<\/strong> is divisible by 3.<\/p>\n\n\n\n<p>We are given <strong>3812<\/strong>*. Let&#8217;s add the known digits:<\/p>\n\n\n\n<p>3 + 8 + 1 + 2 = <strong>14<\/strong><\/p>\n\n\n\n<p>Let the missing digit be <strong>x<\/strong>.<br>So the total sum of the digits becomes: <strong>14 + x<\/strong><\/p>\n\n\n\n<p>We want <strong>14 + x<\/strong> to be divisible by 3.<\/p>\n\n\n\n<p>Let\u2019s test values of x from 0 to 9:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>14 + 1 = 15 \u2192 Not divisible by 3<\/li>\n\n\n\n<li>14 + 2 = 16 \u2192 Not divisible<\/li>\n\n\n\n<li>14 + 3 = 17 \u2192 Not divisible<\/li>\n\n\n\n<li>14 + 4 = 18 \u2192 <strong>Divisible by 3<\/strong><\/li>\n\n\n\n<li>14 + 5 = 19 \u2192 Not divisible<\/li>\n\n\n\n<li>14 + 6 = 20 \u2192 Not divisible<\/li>\n\n\n\n<li>14 + 7 = 21 \u2192 <strong>Divisible by 3<\/strong><\/li>\n\n\n\n<li>14 + 8 = 22 \u2192 Not divisible<\/li>\n\n\n\n<li>14 + 9 = 23 \u2192 Not divisible<\/li>\n\n\n\n<li>14 + 0 = 14 \u2192 Not divisible<\/li>\n<\/ul>\n\n\n\n<p>So the values of x that make <strong>3812x divisible by 3<\/strong> are:<br><strong>x = 4 or x = 7<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2728 Explanation <\/h3>\n\n\n\n<p>This problem explores the rules of divisibility, which are quick mental math shortcuts to determine whether a number can be divided evenly by another number without a remainder. These rules are useful in many math problems and exams.<\/p>\n\n\n\n<p>First, for <strong>divisibility by 8<\/strong>, the rule is to look only at the last three digits of the number. This is because 1,000 is divisible by 8, so anything before the last three digits won\u2019t affect the divisibility by 8. In the number <strong>67,108<\/strong>, the last three digits are <strong>108<\/strong>. When 108 is divided by 8, it gives 13.5, which is not a whole number. This means 108 is not divisible by 8, and therefore, neither is 67,108. The original statement that &#8220;no, 67108 cannot be divisible&#8221; is correct, but the explanation should specifically mention checking the last three digits.<\/p>\n\n\n\n<p>Next, for <strong>divisibility by 3<\/strong>, we use a different rule: A number is divisible by 3 if the <strong>sum of its digits<\/strong> is divisible by 3. In this case, we are given the number 3812*, with the last digit missing. By adding the known digits (3 + 8 + 1 + 2 = 14), we can find which digit should replace the asterisk (*) so that the total sum is divisible by 3. Adding different digits from 0 to 9, we find that adding 4 or 7 gives sums (18 and 21, respectively) that are divisible by 3. So the missing digit must be <strong>4 or 7<\/strong>.<\/p>\n\n\n\n<p>Understanding and applying these simple divisibility rules makes solving such problems much quicker and more efficient.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner7-13.jpeg\" alt=\"\" class=\"wp-image-223009\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>4 b Is 67 108 divisible by 8? Give a reason for your answer. no 67108 cannot be divisible The number 3812* is divisible by 3. The final digit is missing. What can you say about the missing digit?4 b Is 67 108 divisible by 8? Give a reason for your answer. no 67108 cannot [&hellip;]<\/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-223008","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223008","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=223008"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223008\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}