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[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n
A method to find out that any given number is divisible by 7 without actually dividing the number by 7 is the 7 Divisibility rule.<\/span><\/p>\n The steps to check the divisibility are:<\/b><\/p>\n By looking at the multiples of 7, for example, 7, 14, 21, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, etc., we know which numbers are divisible by 7.<\/span><\/p>\n Now let us consider a 3-digit number, 259.<\/span><\/p>\n The last digit of the number is 9, now 2 \u00d7 9 = 18.<\/span><\/p>\n The remaining part of the number 259, is 25. Subtracting 18 from 25 and checking if the result is divisible by 7.<\/span><\/p>\n 25 – 18 = 7,<\/span> which is 7 itself.<\/span><\/p>\n Hence, 259 is divisible by 7 which has been checked by the 7 divisibility rule.\u00a0<\/span><\/p>\n This was easy as the number was small. Now, what should be done if a bigger number is given?<\/span><\/p>\n Within 3 steps it cannot be determined if the number is divisible by 7 or not. For that, we keep on repeating the steps till we get closer to a number about which we are sure to be divisible by 7.<\/span><\/p>\n Let us consider a large number, <\/span>19915<\/span>.<\/span><\/p>\n The last digit of the number is <\/span>5<\/span>, now <\/span>2 \u00d7 5 = 10<\/span>.<\/span><\/p>\n The remaining part of the number <\/span>19915<\/span>, is <\/span>1991<\/span>. Subtracting <\/span>10<\/span> from <\/span>1991<\/span> and checking if the result is divisible by <\/span>7<\/span>.<\/span><\/p>\n 1991 – 10 = 1981<\/span>,<\/span>\u00a0<\/span><\/p>\n Which is a large number and we don\u2019t know it is divisible by <\/span>7<\/span>, so we repeat the steps from the first step. This time we take <\/span>1981<\/span> as the number.<\/span><\/p>\n The last digit of the number is <\/span>1<\/span>, now <\/span>2 \u00d7 1 = 2<\/span>.<\/span><\/p>\n The remaining part of the number <\/span>1981<\/span>, is <\/span>198<\/span>.<\/span><\/p>\n Subtracting <\/span>2<\/span> from <\/span>198<\/span> and checking if the result is divisible by <\/span>7<\/span>.<\/span><\/p>\n 198 – 2 = 196,<\/span>\u00a0<\/span><\/p>\n Again, we don\u2019t know it is divisible by <\/span>7<\/span>, so we repeat the steps from the first step. This time we take <\/span>196<\/span> as the number.<\/span><\/p>\n The last digit of the number is <\/span>6<\/span>, now <\/span>2 \u00d7 6 = 12<\/span>.<\/span><\/p>\n The remaining part of the number <\/span>196<\/span>, is <\/span>19<\/span>.<\/span><\/p>\n Subtracting <\/span>12<\/span> from <\/span>19<\/span> and checking if the result is divisible by <\/span>7<\/span>.<\/span><\/p>\n 19 – 12 = 7,<\/span> which is <\/span>7<\/span> itself.\u00a0<\/span><\/p>\n Hence, <\/span>19915<\/span> is divisible by <\/span>7<\/span> which has been checked by the divisibility test.<\/span><\/p>\n <\/p>\n Example 1<\/strong>:<\/strong> Using the divisibility rule of <\/span>7<\/span>, can you determine if <\/span>36687<\/span> is divisible by <\/span>7<\/span>?<\/span><\/p>\n Solution:<\/strong><\/p>\n The last digit of the number <\/span>36687<\/span> is <\/span>7<\/span>.<\/span><\/p>\n To double the last digit, we multiply it by <\/span>2<\/span> i.e., <\/span>7 \u00d7 2 = 14<\/span>.<\/span><\/p>\n 14<\/span> is subtracted from the remaining number that is <\/span>3668<\/span>.<\/span><\/p>\n 3668 – 14 = 3654<\/span><\/p>\n Repeating the steps again because if <\/span>3654<\/span> is divisible by <\/span>7<\/span> is not known.<\/span><\/p>\n The last digit of the number is <\/span>4<\/span>.<\/span><\/p>\n To double the last digit, we multiply it by <\/span>2<\/span> i.e., <\/span>4 \u00d7 2 = 8<\/span>.<\/span><\/p>\n 8<\/span> is subtracted from the remaining number that is <\/span>365<\/span>.<\/span><\/p>\n 365 – 8 = 357<\/span><\/p>\n Again, the steps are repeated because if <\/span>357<\/span> is divisible by <\/span>7<\/span> is not known.<\/span><\/p>\n The last digit of the number is <\/span>7<\/span>.<\/span><\/p>\n To double the last digit, we multiply it by <\/span>2<\/span> i.e., <\/span>7 \u00d7 2 = 14<\/span>.<\/span><\/p>\n 14<\/span> is subtracted from the remaining number that is <\/span>35<\/span>.<\/span><\/p>\n 35 – 14 = 28<\/span><\/p>\n 28 = 7 \u00d7 4<\/span>, hence we can say that <\/span>36687<\/span> is divisible by <\/span>7<\/span>.<\/span><\/span><\/p>\n <\/span><\/p>\n Example <\/strong>2:<\/strong> Rita has <\/span>343<\/span> stickers in her collection, she wants to arrange the stickers in such a manner that there are <\/span>7<\/span> stickers in one row. Check by divisibility test if it is possible to do so without any row being left incomplete.<\/span><\/p>\n Solution:<\/strong><\/p>\n To check if it is possible to arrange <\/span>343<\/span> stickers in a row of <\/span>7<\/span> we use the divisibility rule of <\/span>7<\/span>.<\/span><\/p>\n The last digit of the number <\/span>343<\/span> is <\/span>7<\/span>.<\/span><\/p>\n To double the last digit, we multiply it by <\/span>2<\/span> i.e., <\/span>3 \u00d7 2 = 6<\/span>.<\/span><\/p>\n 6<\/span> is subtracted from the remaining number that is <\/span>34<\/span>.<\/span><\/p>\n 34 – 6 = 28<\/span><\/p>\n 28 = 7 \u00d7 4<\/span>, hence we can say that <\/span>343<\/span> is divisible by <\/span>7<\/span>.<\/span><\/p>\n Rita can arrange her stickers in such a manner that each row contains <\/span>7<\/span>\n
Examples<\/b><\/h2>\n