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Any number is a factor of a number if it divides the number without leaving any remainder behind. If two or more numbers share factors, i.e., a few of their factors are the same then the factors are termed as common factors.<\/span><\/p>\n For example,<\/span><\/p>\n The factors of 30 are 1, 2, 3, 5, 6, 10 and 15.<\/span><\/p>\n The factors of 35 are 1, 5, 7 and 35.<\/span><\/p>\n Here, \u20181\u2019 and \u20185\u2019 are the factors that are common for both 30 and 35. These factors are common factors.<\/span><\/span><\/p>\n Note:<\/strong> \u20181\u2019 is a common factor of any two numbers. Even if two numbers share no factors in common they will always have \u20181\u2019 as a common factor. These numbers are mutually prime or co-prime.<\/span><\/p>\n <\/p>\n The steps to determine the common factors are:<\/span><\/p>\n <\/span><\/p>\n For example:<\/strong><\/p>\n To determine the common factors of 45 and 60, at first, we write down the factors of 45 and 60.<\/span><\/p>\n Factors of\u00a0 45 are 1<\/strong>, 3<\/strong>, 5<\/strong>, 9, 15<\/strong> and 45.<\/span><\/p>\n Factors of 60 are\u00a0 1<\/strong>, 2, 3<\/strong>, 4, 5<\/strong>, 6, 10, 12, 15<\/strong>, 20, 30 and 60.<\/span><\/p>\n Hence the factors that are common for both are 1, 3, 5 and 15 which are the common factors of 45 and 60.\u00a0<\/span><\/p>\n <\/span><\/p>\n After the common factors of a group of 2 or more numbers are determined the largest of those factors is known as the Greatest Common Factor (GCF). It is also known as the Highest Common Factor ( HCF).<\/span><\/p>\n For example, let us consider two numbers 56 and 84.<\/span><\/p>\n At first, we write down the factors of 56 and 84.<\/span><\/p>\n Factors of 56 are 1<\/strong>, 2<\/strong>, 4<\/strong>, 7<\/strong>, 8, 14<\/strong>, 28<\/strong> and 56.<\/span><\/p>\n Factors of 84 are\u00a0 1<\/strong>, 2<\/strong>, 3, 4<\/strong>, 6, 7<\/strong>, 12, 14<\/strong>, 21, 28<\/strong>, 42 and 84.<\/span><\/p>\n Hence the factors that are common for both are 1, 2, 4, 7, 14 and 28 which are the common factors of 56 and 84.<\/span><\/p>\n Now among the common factors, 28 is the greatest. Therefore, 28 is the GCF or 56 and 84.\u00a0\u00a0<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example 1<\/strong>: <\/strong>What are the common factors of 24, 56 and 72?<\/span><\/p>\n Solution:<\/strong><\/p>\n Identifying the factors of each number first,<\/span><\/p>\n Factors of 24 are 1, 2, 4, 6, 8, 12 and 24.<\/span><\/p>\n Factors of 56 are\u00a0 1, 2, 4, 7, 8, 14, 28 and 56.<\/span><\/p>\n Factors of 72 are\u00a0 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.<\/span><\/p>\n Hence, the common factors are 1, 2, 4, 8 and 12.<\/span><\/p>\n <\/span><\/p>\n Example 2<\/strong>:<\/strong> What is the GCF of 48, 64 and 90?<\/span><\/p>\n Solution:<\/strong><\/p>\n Identifying the factors of each number first,<\/span><\/p>\n Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.<\/span><\/p>\n Factors of 64 are\u00a0 1, 2, 4, 8, 16, 32 and 64.<\/span><\/p>\n Factors of 90 are\u00a0 1, 2, 3, 5, 6,\u00a0 9, 10, 15, 18, 30, 45 and 90.<\/span><\/p>\n The common factors are 1 and 2. Hence the GCF is 2.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example 3<\/strong>:<\/strong> Determine the common factors of 45 and 58.<\/span><\/p>\n Solution:<\/strong><\/p>\n Writing down the factors of each number first,<\/span><\/p>\n Factors of 45 are\u00a0 1, 3, 5, 9, 15 and 45.<\/span><\/p>\n Factors of 58 are\u00a0 1, 2, 29 and 58.<\/span><\/p>\n Hence the numbers 45 and 58 have just 1 as a common factor.<\/span><\/p>\n Note<\/b>: 45 and 58 are coprime as they have only \u20181\u2019 as their common factor.<\/span><\/p>\n [\/et_pb_text][et_pb_text _builder_version=”4.11.3″ _module_preset=”default” custom_padding=”||56px|||” global_colors_info=”{}”][\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\nHow to determine common factors of the given numbers?<\/b><\/h2>\n
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Greatest Common Factor<\/b><\/h2>\n
Examples<\/b><\/h2>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n