{"id":2625,"date":"2021-10-05T09:05:01","date_gmt":"2021-10-05T09:05:01","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2625"},"modified":"2021-10-05T10:24:43","modified_gmt":"2021-10-05T10:24:43","slug":"understanding-co-prime-numbers","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/understanding-co-prime-numbers\/","title":{"rendered":"UNDERSTANDING CO-PRIME NUMBERS"},"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;4.11.1&#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; hover_enabled=&#8221;0&#8243; 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; sticky_enabled=&#8221;0&#8243;]<\/p>\n<h1><strong>UNDERSTANDING CO-PRIME NUMBERS<\/strong><\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.11.1&#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||4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><b>WHAT ARE CO-PRIME NUMBERS?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Any two numbers can be co-prime numbers when they only have one factor in common which is the number 1. We need at least two numbers to form a set of these co-prime numbers. Consider the numbers 5 and 7. They have only one factor in common which is the number 1 so these are co-prime numbers.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<h2><b>CO-PRIME AND PRIME NUMBERS<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Co-prime numbers are different from prime numbers. While prime numbers have only two factors which are the 1 and the number itself, it is not the case with co-prime numbers. Co-prime numbers are a set of numbers that only have 1 as their common factor.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<h3><b>HOW TO FIND CO-PRIME NUMBERS?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">The easiest way to find a co-prime number is to find out the <\/span><b><i>HCF or highest common factor<\/i><\/b><span style=\"font-weight: 400;\">. The highest common factor is the greatest possible number which divides both the numbers exactly. So, <\/span><b><i>if the highest common factor between two or more numbers is 1 then they are co-prime numbers<\/i><\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h3><b>PROPERTIES OF CO-PRIME NUMBERS<\/b><\/h3>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Any two prime numbers are co-primes. {for example: (5,7), (2, 11)}.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The set of co-prime numbers can have one prime and one composite number {for example: (4,7), (2,9)}<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The set can also be made with both composite numbers (numbers that are not prime are called composite numbers) {for example: (4, 9), (8, 11)}<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The highest common factor of co-prime numbers is always 1.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The number 1 itself is a co-prime with every other number.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The lowest common factor of any two co-prime numbers is simply their product. For example, the LCM of 5 and 7 is (5 x 7) = 35.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Any two consecutive numbers are co-primes. For example, (1,2), (2,3), (3,4).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Any two even numbers can never be co-primes because all even numbers have two or more common factors. For example, (12, 14).<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">\u00a0Numbers that divide 12 completely (factors) are 1, 2, 3, 4, 6, 12.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Numbers that divide 14 completely (factors) are 1, 2, 7, 14. The common factors for 12 and 14 are 1 and 2. Therefore, they are not co-primes.<\/span><\/p>\n<h3><b>CO-PRIME NUMBERS FROM 1 to 100<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Co-prime numbers from 1 to 100 include all the consecutive numbers which are (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10, 11), (11, 12), (12, 13) and so on.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It also includes the set of all prime numbers which are (5,7), (7,11), (13,17), (5,31), (61,11) , (53,11) along with all possible combinations of prime numbers from 1 to 100 ( prime numbers: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Two composite numbers can also form co-prime numbers such as (4,9), (8,15), (16,21) and so on.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A pair of prime and composite numbers that can be co-primes are (3,10), (8, 13), (7, 15), (11, 20) and so on.\u00a0\u00a0\u00a0<\/span><\/p>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Sample Questions<br \/>\n&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;28px&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Practice Multiple Choice Questions<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Question 1&#8243; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; hover_enabled=&#8221;0&#8243; border_radii=&#8221;on|15px|15px|15px|15px&#8221; border_width_all=&#8221;2px&#8221; border_color_all=&#8221;#000000&#8243; border_width_top=&#8221;4px&#8221; border_color_top=&#8221;#E02B20&#8243; global_colors_info=&#8221;{}&#8221; sticky_enabled=&#8221;0&#8243;]<\/p>\n<div class=\"qmanage\">\n<div class=\"qq\">\n<p><strong>Questions<\/strong><\/p>\n<p><b>Example 1<\/b><span style=\"font-weight: 400;\">. Let us consider two numbers, 9 and 11. They can be factorized as follows:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The numbers 9 and 11 have only one common factor which is the number 1. Therefore, (9,11) are co-prime numbers.\u00a0<\/span><\/p>\n<p><b>Example 2.<\/b><span style=\"font-weight: 400;\"> Now think about 11 and 13. They can be factorized as follows:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The numbers 11 and 13 have 1 as their only common factor. Therefore, we can say that 11 and 13 are also co-prime numbers.<\/span><\/p>\n<p><b>Example 3.<\/b><span style=\"font-weight: 400;\"> Let us consider the two numbers 6 and 9. They can be factorized as follows:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The numbers here have two common factors which are 1 and 3. Therefore, they are not co-primes.\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\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;http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/7-days-week-free-trial.jpg&#8221; title_text=&#8221;7-days-week-free-trial&#8221; url=&#8221;https:\/\/mindspark.in\/free-trial&#8221; align=&#8221;center&#8221; module_class=&#8221;adsimg&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; custom_padding=&#8221;||||false|false&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221; transform_styles__hover_enabled=&#8221;on|hover&#8221; transform_scale__hover_enabled=&#8221;on|hover&#8221; transform_translate__hover_enabled=&#8221;on|desktop&#8221; transform_rotate__hover_enabled=&#8221;on|desktop&#8221; transform_skew__hover_enabled=&#8221;on|desktop&#8221; transform_origin__hover_enabled=&#8221;on|desktop&#8221; transform_scale__hover=&#8221;102%|102%&#8221;][\/et_pb_image][et_pb_text admin_label=&#8221;Explore Other Topics<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Explore Other Topics<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.10.6&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a class=\"otherc\" href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/\">Geometry<\/a><\/div>\n<div class=\"trr\"><a class=\"otherc\" href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/\">Trigonometry<\/a><\/div>\n<div class=\"trr\"><span style=\"color: #000000;\"><a href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/\" style=\"color: #000000;\">Operations<\/a><\/span><\/div>\n<div class=\"trr\"><a class=\"otherc\" href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/\">Numbers<\/a><\/div>\n<div class=\"trr\"><span style=\"color: #000000;\"><a href=\"http:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/\" style=\"color: #000000;\">Angles<\/a><\/span><\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Related Concepts<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Related Concepts<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a class=\"otherc\" href=\"#\">Obtuse angle<\/a><\/div>\n<div class=\"trr\"><a class=\"otherc\" href=\"#\">Reflex angle<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;Row for space&#8221; 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_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;4.11.1&#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<p><b>1. Are all prime numbers co-primes?<\/b><\/p>\n<p><b><i>Ans:<\/i><\/b><span style=\"font-weight: 400;\"> Yes! We can pick any two or more prime numbers and they will always be co-primes because the only common factor will be the number 1.\u00a0<\/span><\/p>\n<p><b>2. Are all co-primes prime numbers?<\/b><\/p>\n<p><b><i>Ans:<\/i><\/b><span style=\"font-weight: 400;\"> No. Co-prime numbers can be a set of two prime numbers, two composite numbers or one composite and one prime number.<\/span><\/p>\n<p><b>3. Is 1 a co-prime to all the other numbers?<\/b><\/p>\n<p><b><i>Ans:<\/i><\/b><span style=\"font-weight: 400;\"> Yes! It is so because any other number say 12 has only one factor in common with 1 which is 1 itself.<\/span><\/p>\n<p><b>4. Can any two even numbers be co-prime?<\/b><\/p>\n<p><b><i>Ans:<\/i><\/b><span style=\"font-weight: 400;\"> No. Even numbers are the numbers divisible by 2 so any two even numbers will have 1 and 2 as their common factors but co-prime numbers are those that have only 1 as their common factor.\u00a0<\/span><\/p>\n<p><b>5. Can any two composite numbers be co-primes?<\/b><\/p>\n<p><b><i>Ans:<\/i><\/b><span style=\"font-weight: 400;\"> Yes. There are various examples of two composite numbers being co-primes. For example : (8,15) , (16, 21) , (4,27) and so on.\u00a0<\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Numbers can be expressed in words and we call them number names. The numbers starting from 1 to 20 are written with specific spellings followed by a generic pattern. <\/p>\n","protected":false},"author":7,"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>UNDERSTANDING CO-PRIME NUMBERS - mydomain<\/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:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/understanding-co-prime-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"UNDERSTANDING CO-PRIME NUMBERS - mydomain\" \/>\n<meta property=\"og:description\" content=\"Numbers can be expressed in words and we call them number names. 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