{"id":4244,"date":"2021-11-21T12:24:00","date_gmt":"2021-11-21T12:24:00","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4244"},"modified":"2021-12-14T12:41:53","modified_gmt":"2021-12-14T12:41:53","slug":"finding-relatively-prime-numbers-with-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/finding-relatively-prime-numbers-with-examples\/","title":{"rendered":"FINDING RELATIVELY PRIME NUMBERS WITH EXAMPLES"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>FINDING RELATIVELY PRIME NUMBERS WITH EXAMPLES<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; custom_padding=&#8221;15px|15px|54px|4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><b>RELATIVELY PRIME NUMBERS<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><b>Relatively prime numbers are those which have only one common factor which is the number 1.<\/b><span style=\"font-weight: 400;\"> Now, before we go any further, it is important to understand the meaning of prime numbers. Prime numbers are those which have two factors only, namely the number itself and 1. These numbers are not divisible by any other number. For example, 2, 3, 5, 7, 11, 13, 19 and so on are all prime numbers. The numbers that are not prime are called composite numbers. 1 is neither a prime nor a composite number.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><b>Relatively prime numbers can also be called co-primes or mutually prime numbers.<\/b><span style=\"font-weight: 400;\"> It is a set of numbers that has only 1 as the common divisor. Relatively prime numbers don\u2019t need to be prime numbers only. They can be composite numbers as well or one can be prime and the other can be a composite number.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, c<\/span><span style=\"font-weight: 400;\">onsider the following set of numbers:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>4, 19<\/b><span style=\"font-weight: 400;\"> \u2013 These numbers have only one factor in common which is 1 so they are co-primes. Here, one number is composite and the other is prime.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>2, 7 <\/b><span style=\"font-weight: 400;\">\u2013 They are both prime numbers and the only common divisor is 1. Thus, making them co-prime numbers.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>4, 9<\/b><span style=\"font-weight: 400;\"> \u2013 Though both these numbers are composite, the only factor common among them is 1.<\/span><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h3><b>HOW TO IDENTIFY RELATIVELY PRIME NUMBERS<\/b><\/h3>\n<p><b><\/b><\/p>\n<p><span style=\"font-weight: 400;\">The best way to identify co-primes is <\/span><b>to find the greatest common divisor or the highest common factor (HCF)<\/b><span style=\"font-weight: 400;\">. HCF is simply the highest number that can divide both the numbers into consideration. For example, consider the numbers 18 and 21.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Factors of 18 are 1, 2, 3, 6, 9 and 18.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Factors of 21 are 1, 3, 7, 21.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The common factors are 1 and 3 but the highest of the two is 3 so the HCF of 18 and 21 is 3.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In the case of relatively prime numbers, we can find the HCF and if it is 1 then they are co-primes.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example 6 and 17.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Factors of 6 are 1, 2, 3 and 6.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Factors of 17 are 1, 17.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The only and the highest factor that is common is 1. Therefore, 6 and 17 are mutually prime or relatively prime.<\/span><b><\/b><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; module_id=&#8221;stickysideR&#8221; admin_label=&#8221;Column R&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#fdefe0&#8243; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; sticky_position=&#8221;top&#8221; sticky_offset_top=&#8221;-280px&#8221; sticky_limit_top=&#8221;row&#8221; sticky_limit_bottom=&#8221;row&#8221; sticky_position_tablet=&#8221;none&#8221; sticky_position_phone=&#8221;none&#8221; sticky_position_last_edited=&#8221;on|desktop&#8221; sticky_limit_bottom_tablet=&#8221;&#8221; sticky_limit_bottom_phone=&#8221;&#8221; sticky_limit_bottom_last_edited=&#8221;on|phone&#8221; border_radii=&#8221;on|15px|15px|15px|15px&#8221; box_shadow_style=&#8221;preset3&#8243; global_colors_info=&#8221;{}&#8221;][et_pb_image src=&#8221;https:\/\/eistudymaterial.s3.amazonaws.com\/1080&#215;1080.png&#8221; 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_builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; text_orientation=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"ffmanage\">\n<div class=\"textmanagestyle\">\n<div class=\"fone\">\n<p>Ready to get started ?<\/p>\n<\/div>\n<div class=\"sone\">\n<p class=\"ffbtn\"><a href=\"https:\/\/mindspark.in\/free-trial\">Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png&#8221; title_text=&#8221;down-circle&#8221; show_bottom_space=&#8221;off&#8221; align=&#8221;right&#8221; module_class=&#8221;img2&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; width=&#8221;44px&#8221; height=&#8221;18px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;FAQ Row&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|40px||40px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;FAQ&#8221; module_class=&#8221;faqstyl&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;center&#8221; header_line_height=&#8221;2.5em&#8221; background_color=&#8221;#dbedc6&#8243; max_width=&#8221;80%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_padding=&#8221;30px|25px|30px|25px|true|true&#8221; hover_enabled=&#8221;0&#8243; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221; sticky_enabled=&#8221;0&#8243;]<\/p>\n<h1>Frequently Asked Questions<span style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/h1>\n<ol><\/ol>\n<h3><strong>Q1. Are co-prime numbers different from relatively prime numbers?<br \/><\/strong><\/h3>\n<p><span style=\"font-weight: 400;\"><strong>Ans: <\/strong>No. Relatively prime numbers are also called co-prime numbers or mutually prime numbers.<strong><\/strong><\/span><\/p>\n<h3><strong>Q2. How to find relatively prime numbers?<br \/><\/strong><\/h3>\n<p><strong>Ans: <\/strong><span style=\"font-weight: 400;\">The easiest way to find the relatively prime numbers is to find the highest common factor(HCF) and if the HCF is 1 then they are relatively prime.\u00a0<\/span><\/p>\n<h3><strong>Q3. Are 17 and 89 relatively prime?<\/strong><\/h3>\n<p><strong>Ans: <\/strong><span style=\"font-weight: 400;\">The factors of 17 are 1, 17 and the factors of 89 are 1, 89. The only common factor or HCF is 1 so, yes, they are relatively prime.\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meta Description: We can calculate the sum of the terms in a geometric progression using the formula  S = a(1-r^n)\/(1-r) when r < 1 and  S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>FINDING RELATIVELY PRIME NUMBERS WITH EXAMPLES - mydomain<\/title>\n<meta name=\"description\" content=\"Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r &lt; 1 and S = a(r^n-1)\/(r-1)when r&gt;1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/finding-relatively-prime-numbers-with-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"FINDING RELATIVELY PRIME NUMBERS WITH EXAMPLES - 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