Manuela is looking for all the factors of 90. So far, she has divided 90 by all the counting numbers from 1 to 10, listing those numbers that divide 90 and listing the corresponding quotients. Here is Manuela’s work so far:<\/p>\n\n\n\n
1, 90 1 X 90 = 90
2, 45 2 X 45 = 90
3, 30 3 X 30 = 90
5, 18 5 X 18 = 90
6, 15 6 X 15 = 90
9, 10 9 X 10 = 90
10, 9 10 X 9 = 90
Should Manuela stop dividing at this point? If so, why? What are all the factors of 90?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Answer:<\/strong><\/p>\n\n\n\n Yes, Manuela should stop dividing at this point because she has found all the factor pairs of 90. The factors of 90 are all the numbers that divide 90 evenly without leaving a remainder. The complete list of factors of 90 is:<\/p>\n\n\n\n 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90<\/strong><\/p>\n\n\n\n When finding factors of a number, one efficient method is to check divisors only up to the square root<\/strong> of the number because factors come in pairs. For 90, the square root is approximately: 90\u22489.49\\sqrt{90} \\approx 9.49<\/p>\n\n\n\n This means all factor pairs will include one number less than or equal to 9.49 and one number greater than or equal to 9.49. Manuela has checked all numbers from 1 up to 10, which is just past the square root. Since 10 is already greater than the square root, she has covered the entire range needed.<\/p>\n\n\n\n Looking at Manuela’s pairs:<\/p>\n\n\n\n Because factor pairs repeat after crossing the square root (e.g., 9 \u00d7 10 and 10 \u00d7 9), Manuela does not need to test numbers greater than 10.<\/p>\n\n\n\n From these pairs, the complete list of factors is all unique numbers appearing in the pairs: {1,2,3,5,6,9,10,15,18,30,45,90}\\{1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90\\}<\/p>\n\n\n\n These are all the positive factors of 90.<\/p>\n\n\n\n Manuela is looking for all the factors of 90. So far, she has divided 90 by all the counting numbers from 1 to 10, listing those numbers that divide 90 and listing the corresponding quotients. Here is Manuela’s work so far: 1, 90 1 X 90 = 902, 45 2 X 45 = 903, 30 […]<\/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-214651","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214651","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=214651"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214651\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nExplanation:<\/h3>\n\n\n\n
\n
\n\n\n\nSummary:<\/h3>\n","protected":false},"excerpt":{"rendered":"