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Factors of a number are the numbers that divide the given number completely. Prime numbers only have two factors that are the number itself and 1 whereas composite numbers have more than two factors which also include prime factors. Prime numbers are those numbers that are not divisible by any other number except 1 and the number itself. Non-prime(Composite) numbers are divisible by more than two numbers.<\/span><\/p>\n <\/p>\n <\/b><\/p>\n 13 is a prime number and has only two factors which are 1 and 13.\u00a0<\/span><\/p>\n 36 is a composite number and has more than two factors which are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The ordered pairs are (1 x 36 = 36, 2 x 18 = 36, 3 x 12 = 36, 6 x 6 = 36). Prime factors are the factors that are prime in nature. The number 36 can be expressed as the product of prime factors : 36=3^{2} \\times 2^{2}<\/span><\/span><\/span><\/p>\n <\/p>\n <\/p>\n There are basic formulas for factors of a number N, where N =p^{a} q^{b} r^{c}<\/span> and<\/span>\u00a0p, q and r are the prime factors of a number and a, b and c are positive exponents. They are namely \u2013\u00a0<\/span><\/p>\n Let us look at some examples<\/span><\/p>\n 1.<\/strong> Consider the number 36.<\/b><\/span><\/p>\n The prime factorisation of 36 is 36=2^{2} \\times 3^{2}<\/span>, <\/span>so<\/span> the number of factors of 36 are ( 2+1)(2+1) = 9<\/span><\/p>\n The sum of the factors of 36<\/span><\/p>\n =\\left(\\frac{2^{2+1}-1}{2-1}\\right)\\left(\\frac{3^{2+1}-1}{3-1}\\right)<\/span><\/span><\/p>\n =\\frac{7}{1} \\times \\frac{8}{2}<\/span><\/span><\/p>\n = 28<\/span><\/span><\/p>\n The product of the factors is 36^{9 \/ 2}=1,00,77,696<\/span><\/span><\/span><\/span><\/p>\n <\/span><\/p>\n 2. Consider the number 15 = 5 x 3<\/b><\/p>\n <\/span><\/p>\n The number of factors of 15 are (1+1)(1+1) = 4<\/span><\/p>\n Sum of the factors is \\left(\\frac{5^{1+1}-1}{5-1}\\right)\\left(\\frac{3^{1+1}-1}{3-1}\\right)=24<\/span><\/span><\/p>\n Product of the factors is 15^{4 \/ 2}=225<\/span><\/span><\/p>\n [\/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>\nExamples\u00a0<\/b><\/h2>\n
FORMULAS FOR FACTORS OF A NUMBER<\/b><\/b><\/h2>\n
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EXAMPLES<\/b><\/h2>\n
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