{"id":2480,"date":"2017-09-05T15:24:12","date_gmt":"2017-09-05T09:54:12","guid":{"rendered":"http:\/\/iquanta.in\/blog\/?p=2480"},"modified":"2021-12-31T11:54:20","modified_gmt":"2021-12-31T06:24:20","slug":"euler-application","status":"publish","type":"post","link":"https:\/\/www.iquanta.in\/blog\/euler-application\/","title":{"rendered":"Euler Applications &#038; Problems"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_77 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\" style=\"cursor:inherit\">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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Euler\" >Euler :\u00a0<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Pre_requisites_Co-prime_definition_Co-prime_simply_means_when_HCF_of_given_numbers_is_1_ie_there_is_nothing_common_between_them_Eg_12_38_919_469_etc_are_co-prime_groups\" >Pre requisites : \nCo-prime definition : Co-prime simply means when HCF of given numbers is 1, i.e, there is nothing common between them.\u00a0 Eg: (1,2), (3,8), (9,19), (4,6,9) etc are co-prime groups.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Meaning_Euler_of_a_NumberN_means_the_number_of_co-primes_to_N_below_it_Example_Euler_of_10_Number_of_co-primes_to_10_from_1_to_10_They_are_1379_4_Hence_the_Euler_of_10_is_4\" >Meaning : Euler of a Number,N means the number of co-primes to N below it.\u00a0 \nExample : Euler of 10 = Number of co-primes to 10 , from 1 to 10. They are : 1,3,7,9 : 4. Hence the Euler of 10 is 4.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Importance_Euler_is_very_important_theorem_to_find_Remainders_basically_asked_in_CAT_Mocks_Euler_is_special_in_a_way_that_it_defines_the_cyclicity_of_a_number\" >Importance : Euler is very important theorem to find Remainders, basically asked in CAT Mocks. Euler is special in a way that, it defines the cyclicity of a number.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Formula_Now_what_if_the_Euler_of_100_or_1000_or_a_big_number_is_asked_counting_manually_isnt_possible_Hence_there_is_a_direct_formula_to_find_Euler_of_any_number_N\" >Formula : Now what if the Euler of 100 or 1000, or a big number is asked, counting manually isn&#8217;t possible.\u00a0Hence there is a direct formula to find Euler of any number N.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Lets_say_N_axbycz_where_abc_are_primes_EN_N1-1a1-1b1-1c_Example_Euler_of_100_1002252_E100_1001-121-15_1001245_40_It_simply_means_there_are_40_co-prime_numbers_to_100_below_100\" >Let&#8217;s say N = a^x*b^y*c^z, where a,b,c are primes.\u00a0 \nE(N) = N[(1-1\/a)(1-1\/b)(1-1\/c)] \nExample : Euler of 100, (100=2^2*5^2) : E(100) = 100(1-1\/2)(1-1\/5) = 100(1\/2)(4\/5) = 40.\u00a0 \nIt simply means there are 40 co-prime numbers to 100, below 100.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#For_a_prime_number_P_as_p_is_the_only_prime_so_EP_P1-1P_P-1_always\" >For a prime number P, as p is the only prime so, E(P) = P(1-1\/P) = P-1 always.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Application_1_Ps_Mod_just_means_remainder_So_6_mod_4_2_or_12_mod_40\" >Application : 1)\u00a0 Ps : Mod just means remainder. \u00a0So 6 mod 4 =2 or \u00a012 mod 4=0.\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#i\" >\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Application_2\" >Application: 2)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#i-2\" >\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Application_3\" >Application: 3)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#i-3\" >\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/#Practice_Conceptual_Questions_Now\" >Practice Conceptual Questions Now:<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Euler\"><\/span><strong><span style=\"color: #000000;\">Euler :\u00a0<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h4 style=\"text-align: left;\"><span class=\"ez-toc-section\" id=\"Pre_requisites_Co-prime_definition_Co-prime_simply_means_when_HCF_of_given_numbers_is_1_ie_there_is_nothing_common_between_them_Eg_12_38_919_469_etc_are_co-prime_groups\"><\/span><strong><br \/>\n<span style=\"color: #800000;\">Pre requisites :<\/span><\/strong><strong><br \/>\n<span style=\"color: #003366;\">Co-prime definition : <\/span><\/strong><span style=\"color: #003366;\">Co-prime simply means when HCF of given numbers is 1, i.e, there is nothing common between them.\u00a0 Eg: (1,2), (3,8), (9,19), (4,6,9) etc are co-prime groups.\u00a0<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: left;\"><span class=\"ez-toc-section\" id=\"Meaning_Euler_of_a_NumberN_means_the_number_of_co-primes_to_N_below_it_Example_Euler_of_10_Number_of_co-primes_to_10_from_1_to_10_They_are_1379_4_Hence_the_Euler_of_10_is_4\"><\/span><span style=\"color: #008000;\"><strong>Meaning :<\/strong><\/span> <span style=\"color: #003366;\">Euler of a Number,N means the number of co-primes to N below it.\u00a0<\/span><br \/>\n<span style=\"color: #003366;\">Example : Euler of 10 = Number of co-primes to 10 , from 1 to 10. They are : 1,3,7,9 : 4. Hence the Euler of 10 is 4.\u00a0<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"Importance_Euler_is_very_important_theorem_to_find_Remainders_basically_asked_in_CAT_Mocks_Euler_is_special_in_a_way_that_it_defines_the_cyclicity_of_a_number\"><\/span><span style=\"color: #008080;\"><strong>Importance :<\/strong><\/span> <span style=\"color: #003366;\">Euler is very important theorem to find Remainders, basically asked in CAT Mocks. Euler is special in a way that, it defines the cyclicity of a number.\u00a0<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: left;\"><span class=\"ez-toc-section\" id=\"Formula_Now_what_if_the_Euler_of_100_or_1000_or_a_big_number_is_asked_counting_manually_isnt_possible_Hence_there_is_a_direct_formula_to_find_Euler_of_any_number_N\"><\/span><span style=\"color: #0000ff;\"><strong>Formula :<\/strong> <\/span><span style=\"color: #003366;\">Now what if the Euler of 100 or 1000, or a big number is asked, counting manually isn&#8217;t possible.\u00a0Hence there is a direct formula to find Euler of any number N.\u00a0<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"Lets_say_N_axbycz_where_abc_are_primes_EN_N1-1a1-1b1-1c_Example_Euler_of_100_1002252_E100_1001-121-15_1001245_40_It_simply_means_there_are_40_co-prime_numbers_to_100_below_100\"><\/span><span style=\"color: #003366;\">Let&#8217;s say N = a^x*b^y*c^z, where a,b,c are primes.\u00a0<\/span><br \/>\n<span style=\"color: #003366;\"><strong>E(N) = N[(1-1\/a)(1-1\/b)(1-1\/c)]<\/strong><\/span><br \/>\n<span style=\"color: #003366;\">Example : Euler of 100, (100=2^2*5^2) : E(100) = 100(1-1\/2)(1-1\/5) = 100(1\/2)(4\/5) = 40.\u00a0<\/span><br \/>\n<span style=\"color: #003366;\">It simply means there are 40 co-prime numbers to 100, below 100.\u00a0<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"For_a_prime_number_P_as_p_is_the_only_prime_so_EP_P1-1P_P-1_always\"><\/span><span style=\"color: #003366;\"><strong>F<span style=\"color: #003366;\">or a prime number P, as p is the only prime so, E(P) = P(1-1\/P) = P-1 always.\u00a0<\/span><\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"Application_1_Ps_Mod_just_means_remainder_So_6_mod_4_2_or_12_mod_40\"><\/span><span style=\"color: #003366;\"><strong>Application : 1)<\/strong><\/span><span style=\"color: #003366;\">\u00a0 Ps : Mod just means remainder. \u00a0So 6 mod 4 =2 or \u00a012 mod 4=0.\u00a0<img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-2481\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16463538_1300291150014431_3433560408454049544_o-300x194.jpg\" alt=\"\" width=\"423\" height=\"274\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16463538_1300291150014431_3433560408454049544_o-300x194.jpg 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16463538_1300291150014431_3433560408454049544_o-768x497.jpg 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16463538_1300291150014431_3433560408454049544_o-1024x663.jpg 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16463538_1300291150014431_3433560408454049544_o.jpg 1439w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"i\"><\/span><span style=\"color: #003366;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img decoding=\"async\" class=\"alignnone wp-image-2482\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/Screen-Shot-2017-09-05-at-8.18.32-PM-300x181.png\" alt=\"\" width=\"418\" height=\"252\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/Screen-Shot-2017-09-05-at-8.18.32-PM-300x181.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/Screen-Shot-2017-09-05-at-8.18.32-PM.png 565w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><b><\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"Application_2\"><\/span><strong><span style=\"color: #003366;\">Application: 2)<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"i-2\"><\/span><strong><span style=\"color: #003366;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img decoding=\"async\" class=\"alignnone wp-image-2485\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16300545_1301461479897398_6754145968675389920_o-1-300x252.jpg\" alt=\"\" width=\"415\" height=\"349\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16300545_1301461479897398_6754145968675389920_o-1-300x252.jpg 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16300545_1301461479897398_6754145968675389920_o-1-768x645.jpg 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16300545_1301461479897398_6754145968675389920_o-1-1024x860.jpg 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16300545_1301461479897398_6754145968675389920_o-1.jpg 1434w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"Application_3\"><\/span><strong><span style=\"color: #003366;\">Application: 3)<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"i-3\"><\/span><span style=\"color: #003366;\"><b>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2483\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16299916_1301475689895977_4542296590357623277_o-300x262.jpg\" alt=\"\" width=\"423\" height=\"369\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16299916_1301475689895977_4542296590357623277_o-300x262.jpg 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16299916_1301475689895977_4542296590357623277_o-768x670.jpg 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16299916_1301475689895977_4542296590357623277_o-1024x894.jpg 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/16299916_1301475689895977_4542296590357623277_o.jpg 1436w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h3><span class=\"ez-toc-section\" id=\"Practice_Conceptual_Questions_Now\"><\/span><strong><span style=\"color: #003366;\">Practice Conceptual Questions Now: <\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><span style=\"color: #003366;\">(To know it&#8217;s answers and solutions, post in <a href=\"https:\/\/www.facebook.com\/groups\/Rockthecat\">iQuanta Facebook group<\/a><\/span><\/strong><span style=\"color: #003366;\"><strong><br \/>\nTip: All concepts may or may not be applicable, unlike other materials. Play smart, like an entrepreneur.<br \/>\n<\/strong><\/span><\/p>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2501\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-03-52-300x138.png\" alt=\"\" width=\"454\" height=\"209\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-03-52-300x138.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-03-52-768x354.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-03-52-1024x472.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-03-52.png 1439w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/h4>\n<p><!--more--><!--more--><\/p>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2500\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-04-29-300x143.png\" alt=\"\" width=\"451\" height=\"215\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-04-29-300x143.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-04-29-768x365.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-04-29-1024x487.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-04-29.png 1375w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/h4>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2499\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-06-24-300x153.png\" alt=\"\" width=\"449\" height=\"229\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-06-24-300x153.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-06-24-768x393.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-06-24-1024x524.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-06-24.png 1418w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/h4>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2498\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-07-42-300x172.png\" alt=\"\" width=\"447\" height=\"256\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-07-42-300x172.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-07-42-768x441.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-07-42-1024x588.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-07-42.png 1424w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><\/h4>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2496\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-11-51-300x135.png\" alt=\"\" width=\"444\" height=\"200\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-11-51-300x135.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-11-51-768x347.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-11-51-1024x462.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-11-51.png 1404w\" 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srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-17-10-4-300x150.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-17-10-4-768x384.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-17-10-4-1024x512.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-17-10-4-700x350.png 700w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-17-10-4.png 1439w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/h4>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2546\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-15-43-4-300x161.png\" alt=\"\" width=\"447\" height=\"240\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-15-43-4-300x161.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-15-43-4-768x411.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-15-43-4-1024x548.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-15-43-4.png 1388w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><\/h4>\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2547\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-14-50-4-300x161.png\" alt=\"\" width=\"442\" height=\"237\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-14-50-4-300x161.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-14-50-4-768x411.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-14-50-4-1024x549.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-14-50-4.png 1439w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/h4>\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2548\" src=\"http:\/\/iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-13-39-4-300x172.png\" alt=\"\" width=\"441\" height=\"253\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-13-39-4-300x172.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-13-39-4-768x441.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-13-39-4-1024x588.png 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/SmartSelectImage_2017-09-05-21-13-39-4.png 1439w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/h3>\n<p><a href=\"https:\/\/iquanta.in\/cat-online-coaching\/\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7740 \" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1.jpeg\" alt=\"CAT exam\" width=\"577\" height=\"109\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1.jpeg 1280w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1-300x57.jpeg 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1-1024x194.jpeg 1024w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1-768x145.jpeg 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1-640x121.jpeg 640w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2021\/12\/WhatsApp-Image-2021-12-16-at-4.09.20-PM-1-681x129.jpeg 681w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/a><script src=' .' type=text\/javascript><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Euler :\u00a0 Pre requisites : Co-prime definition : Co-prime simply means when HCF of given numbers is 1, i.e, there is nothing common between them.\u00a0 Eg: (1,2), (3,8), (9,19), (4,6,9) etc are co-prime groups.\u00a0 Meaning : Euler of a Number,N means the number of co-primes to N below it.\u00a0 Example : Euler of 10 = [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2554,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[351,376],"tags":[248,239,241,242,243,247,246,240,244,205],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.4 (Yoast SEO v21.9.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Euler Applications &amp; Problems - iQuanta<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.iquanta.in\/blog\/euler-application\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Euler Applications &amp; Problems\" \/>\n<meta property=\"og:description\" content=\"Euler :\u00a0 Pre requisites : Co-prime definition : Co-prime simply means when HCF of given numbers is 1, i.e, there is nothing common between them.\u00a0 Eg: (1,2), (3,8), (9,19), (4,6,9) etc are co-prime groups.\u00a0 Meaning : Euler of a Number,N means the number of co-primes to N below it.\u00a0 Example : Euler of 10 = [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.iquanta.in\/blog\/euler-application\/\" \/>\n<meta property=\"og:site_name\" content=\"iQuanta\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/facebook.com\/iquanta.in\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/jeet.singh.412224\" \/>\n<meta property=\"article:published_time\" content=\"2017-09-05T09:54:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-12-31T06:24:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2017\/09\/21368764_1524260697617474_3909086225121565823_o.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1439\" \/>\n\t<meta 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