What is the remainder of 74 divided by 7<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the remainder of ( 74 \\div 7 ), we can follow a straightforward division process. When dividing two integers, the remainder is the amount left over after dividing the dividend by the divisor.<\/p>\n\n\n\n Alternatively, we can use modular arithmetic to confirm our answer. The expression ( 74 \\mod 7 ) asks for the remainder when 74 is divided by 7.<\/p>\n\n\n\n Using the formula: Thus, the remainder of ( 74 \\div 7 ) is indeed 4<\/strong>.<\/p>\n\n\n\n In summary, we determined the remainder through direct division, multiplication, and subtraction, verifying our answer with modular arithmetic. Understanding how to compute the remainder is essential in mathematics, particularly in number theory and programming, where such operations frequently occur.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the remainder of 74 divided by 7 The Correct Answer and Explanation is : To find the remainder of ( 74 \\div 7 ), we can follow a straightforward division process. When dividing two integers, the remainder is the amount left over after dividing the dividend by the divisor. Step-by-Step Calculation Verification Using […]<\/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-159761","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159761","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=159761"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159761\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159761"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159761"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-Step Calculation<\/h3>\n\n\n\n
\n
[
74 \\div 7 = 10.57142857 \\ldots
]
This indicates that 7 goes into 74 a total of 10 whole times.<\/li>\n\n\n\n
[
10 \\times 7 = 70
]
This product represents the largest multiple of 7 that is less than or equal to 74.<\/li>\n\n\n\n
[
74 – 70 = 4
]
Thus, the remainder is 4.<\/li>\n<\/ol>\n\n\n\nVerification Using Modular Arithmetic<\/h3>\n\n\n\n
[
a \\mod b = a – (b \\times \\text{floor}(a\/b))
]
where ( \\text{floor}(a\/b) ) is the greatest integer less than or equal to ( a\/b ). In our case, we have:
[
74 \\mod 7 = 74 – (7 \\times 10) = 74 – 70 = 4
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n