{"id":155778,"date":"2022-03-26T01:01:26","date_gmt":"2022-03-25T19:31:26","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/euclid-division-lemma\/"},"modified":"2023-05-12T16:11:32","modified_gmt":"2023-05-12T10:41:32","slug":"euclid-division-lemma","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/","title":{"rendered":"Euclid Division Lemma"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/#Euclid_Division_Algorithm\" title=\"Euclid Division Algorithm\">Euclid Division Algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/#State_Euclids_Division_Lemma\" title=\"State Euclid\u2019s Division Lemma\">State Euclid\u2019s Division Lemma<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/#Euclid_Division_Lemma_Definition\" title=\"Euclid Division Lemma Definition\">Euclid Division Lemma Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/#Euclids_Division_Algorithm\" title=\"Euclid\u2019s Division Algorithm:\">Euclid\u2019s Division Algorithm:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/#Using_Euclids_Division_Algorithm_for_Finding_HCF\" title=\"Using Euclid\u2019s Division Algorithm for Finding HCF\">Using Euclid\u2019s Division Algorithm for Finding HCF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/euclid-division-lemma\/#Euclids_Lemma\" title=\"Euclid\u2019s Lemma:\">Euclid\u2019s Lemma:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Euclid_Division_Algorithm\"><\/span>Euclid Division Algorithm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>The Euclidean division algorithm states that given two positive integers a and b, there is a unique integer q such that a = bq + r, where 0 \u2264 r &lt; b. In other words, the algorithm finds the quotient and remainder when a is divided by b.<\/strong><\/p>\n<p>The algorithm proceeds as follows:<\/p>\n<p>1. Find the largest integer k that is less than or equal to b and divide a by k to get a quotient q and a remainder r.<\/p>\n<p>2. If r = 0, then q is the desired quotient and a is the desired remainder.<\/p>\n<p>3. If r \u2260 0, then replace a and b with q and r, respectively, and go back to step 1.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155777 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/euclid-division-lemma.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/euclid-division-lemma.jpg?v=1648236683 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/euclid-division-lemma-300x212.jpg?v=1648236683 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"State_Euclids_Division_Lemma\"><\/span>State Euclid\u2019s Division Lemma<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Euclidean division lemma states that for every integer a there exists a unique integer q such that a = q*b + r, where b is the integer closest to a and r is the remainder when a is divided by b.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Euclid_Division_Lemma_Definition\"><\/span>Euclid Division Lemma Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Given two positive integers, a and b, there exists a unique integer, c, such that a = cb.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Euclids_Division_Algorithm\"><\/span>Euclid\u2019s Division Algorithm:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>This is an algorithm that is used to divide two numbers. The algorithm is as follows:<\/p>\n<p>If the two numbers are not evenly divisible, then the result will be the quotient and the remainder.<\/p>\n<p>If the two numbers are evenly divisible, then the result will be the whole number that is the result of dividing the two numbers.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Using_Euclids_Division_Algorithm_for_Finding_HCF\"><\/span>Using Euclid\u2019s Division Algorithm for Finding HCF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Given two positive integers a and b, the highest common factor (HCF) of a and b is the largest positive integer that divides both a and b without leaving a remainder.<\/p>\n<p>The division algorithm is a method for finding the HCF of two numbers. The algorithm is as follows:<\/p>\n<p>1. Divide a by b.<\/p>\n<p>2. If a is not divisible by b, then go to step 1.<\/p>\n<p>3. If a is divisible by b, then the HCF of a and b is b.<\/p>\n<p>The following example illustrates how to use the division algorithm to find the HCF of 24 and 15.<\/p>\n<p>1. Divide 24 by 15.<\/p>\n<p>2. 24 is not divisible by 15, so go to step 1.<\/p>\n<p>3. 15 is divisible by 3, so the HCF of 24 and 15 is 3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Euclids_Lemma\"><\/span>Euclid\u2019s Lemma:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In a triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.<\/p>\n<p>The first step is to identify the problem. This may be done through a process of self-evaluation, talking to friends and family, or seeking professional help.<\/p>\n<p>Once the problem is identified, the next step is to develop a plan to address it. This may include making lifestyle changes, seeking counseling or therapy, or taking medication.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Euclid Division Algorithm The Euclidean division algorithm states that given two positive integers a and b, there is a unique [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Euclid Division Lemma","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn Euclid Division Lemma topic of Maths in details explained by subject experts on infinitylearn.com. 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