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A number is divisible by 13 if it leaves zero as the remainder when divided by 13. Here we will understand the divisibility rule of 13 with some examples.<\/p>\n
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<\/b><\/p>\nThe Divisibility Rule of 13<\/b><\/h2>\n
The divisibility rule of 13 helps us know if a number can be divided by 13 without doing the long division process. There are 4 divisibility rules of 13. Let’s know about them one by one:<\/span><\/p>\n <\/p>\n <\/b><\/p>\n Starting from the right (ones place), make a group of the given numbers into sets of 3.<\/span><\/p>\n From the rightmost group, subtract the first set from the second set and then add the remaining digit(s).\u00a0<\/span><\/p>\n Now calculate the results. If the result is either 0 or a number divided by 13 wholly, the given number will be divisible by 13.<\/span><\/p>\n For example: <\/b>In the number <\/span>1153854<\/b> f<\/span>rom the rightmost side, we have:<\/span><\/p>\n First set of 3 numbers = <\/span>854<\/b><\/p>\n Second set = <\/span>153<\/b>, and the remaining digit = <\/span>1<\/b>.<\/span><\/p>\n Subtracting the first and second sets, we get <\/span>854 – 153 = 701<\/b><\/p>\n Now add the remaining digit, we get <\/span>701 + 1 = 702<\/b><\/p>\n The result <\/span>702<\/b>\u00a0is divisible by <\/span>13<\/b>.<\/p>\n Therefore, <\/span>1153854<\/b> is divisible by <\/span>13<\/b>.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n Multiply the last digit of the given number by 4 and add the product with the rest of the number to the left of the last digit.\u00a0<\/span><\/p>\n If the resulting number is either a 0 or divisible by 13, the given number will be divisible by 13.<\/span><\/p>\n For example:<\/b> In the number <\/span>533<\/b>, the unit place digit is <\/span>3<\/b>.\u00a0<\/span><\/p>\n Multiplying it by 4, we get (<\/span>3 x 4<\/b>), which is <\/span>12<\/b>.\u00a0<\/span><\/p>\n Adding 12 to the rest of the digits to the left, we get <\/span>53 + 12 = 65<\/b>.\u00a0<\/span><\/p>\n Since <\/span>65<\/b> is a multiple of <\/span>13.<\/b><\/p>\n Hence <\/span>533<\/b> is divisible by <\/span>13.<\/b><\/p>\n <\/p>\n <\/b><\/p>\n Take the number formed by the last two digits of the given number.\u00a0<\/span><\/p>\n Multiply the rest of the number to the left of these two digits by 4.\u00a0<\/span><\/p>\n Now subtract the number formed by the last two digits from the product.\u00a0<\/span><\/p>\n If the resulting number is either 0 or a multiple of 13, we can confirm that the number is divisible by 13.\u00a0<\/span><\/p>\n For example:<\/b> In the number<\/span> 611<\/b>, the last two digits are <\/span>11.<\/b>\u00a0<\/span><\/p>\n Product of 4 and the rest of the number (<\/span>6<\/b>) is <\/span>6 x 4 = 24.\u00a0<\/b><\/p>\n On subtracting them, we get <\/span>24 – 11<\/b>, which is <\/span>13<\/b> (a multiple of 13).\u00a0<\/span><\/p>\n Therefore, <\/span>611<\/b> is divisible by <\/span>13.<\/b><\/p>\n <\/p>\n <\/b><\/p>\n Multiply the last digit by 9. Now subtract the product and the rest of the number to the left of the last digit. If the difference is either 0 or a multiple of 13, we can confirm that the given number is divisible by 13.<\/span><\/p>\n For example:<\/b> In the number <\/span>676<\/b>, multiplying the last digit (<\/span>6<\/b>) with<\/span> 9<\/b>, we get <\/span>6 x 9<\/b>, which is <\/span>54<\/b>. On subtracting this from the rest of the number, which is <\/span>67<\/b>, we get <\/span>67 – 54<\/b>, which is <\/span>13<\/b>.\u00a0<\/span><\/p>\n Since 13 is a multiple of 13, we can say that <\/span>676<\/b> is divisible by <\/span>13.<\/b><\/p>\n <\/b><\/p>\n Note –<\/b> If the given number is large. If we are unsure if the resultant number obtained from any of the above rules is a multiple of 13, we repeat the divisibility test until we reach a number that can be checked easily from the multiplication table of 13 whether it’s divisible by 13 or not.<\/span><\/p>\n For Example:<\/b>\u00a0Using the divisibility rule of 13, find if <\/span>2782<\/b> is divisible by 13 or not.<\/span><\/p>\n Follow the below steps to check for the divisibility of 13 –\u00a0<\/span><\/p>\n 26<\/b> is divisible by 13.<\/b> Therefore, 2782<\/b> is divisible by 13.<\/b><\/span><\/p>\n <\/b><\/span><\/p>\n <\/p>\n <\/b><\/span><\/p>\n Multiply the last digit of 59371 by 9, which is <\/span>9 \u00d7 1 = 9.<\/span><\/p>\n The remaining number left = 5937<\/span><\/p>\n Subtract 9 from 5937, <\/span>5937 – 9 = 5928.\u00a0<\/span><\/p>\n We are not sure if 5928 is a multiple of 13. <\/span>Let us repeat the process.<\/span><\/p>\n Multiply the last digit of 5928 by 9, which is 8 \u00d7 9 = 72.<\/span><\/p>\n Find the difference between 592 and 72, which is 592 – 72 = 520.\u00a0<\/span><\/p>\n We are still not sure if 520 is a multiple of 13. Let us repeat the process.<\/span><\/p>\n Multiply the last digit of 520 by 9, which is 0 \u00d7 9 = 0.<\/span><\/p>\n Find the difference between 52 and 0, which is 52, a multiple of 13.\u00a0<\/span><\/p>\n Therefore, 59371 is divisible by 13.<\/span><\/p>\n <\/p>\n After grouping the number into sets of 3,\u00a0<\/span><\/p>\n First set from the rightmost = 580<\/span><\/p>\n Second set = 063<\/span><\/p>\n Remaining digit = 3<\/span><\/p>\n Subtracting the first and second sets, we get 580 – 63 = 517<\/span><\/p>\n Adding the remaining digit, we get 517 + 3 = 520<\/span><\/p>\n When 520 is divided by 13, we get the remainder as 0. Hence, 3063580 is divisible by 13.<\/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>\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>\nFirst Rule:<\/b><\/h3>\n
Second Rule:<\/b><\/h3>\n
Third Rule:<\/b><\/h3>\n
Fourth Rule:<\/b><\/h3>\n
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Example:<\/b><\/span><\/h2>\n
1. <\/span>Using the divisibility rule of 13, find if 59371 is divisible by 13 or not?<\/span><\/h3>\n
2. Check if 3063580 is divisible by 13 or not.<\/span><\/h3>\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