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Published on December 7th, 2010 In category Division and Multiplication tricks | Education | Maths

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easy rules for divisibility by 7

An easy way of finding out if the given number is entirely divisible by number  7 or not

The rule for finding out the divisibility is not so straight.

For the smaller numbers i.e with 3 digits (for ex. 273 ) use the following rule :  Double the last digit (3) – reuslt is 6 . Subtract 6 from 27 i.e. 27-6 =21, since 21 is a multiple of 7. The number 273 in entirely divisible from 7

For larger numbers this trick will not work so there is another way

Use the following co-efficients (1,2 and 3) to yeild the results. We multiply the first number starting from the first place by 1, then the second from the right by 3, the third by 2, the fourth by -1, the fifth by -3, the sixth by -2, and the seventh by 1, and so forth.

So if you have number  kjihgfedcba – then do the following – (mind you the multiplation start from right to left from units place)

(a x 1) + (b x 3) +(c x 2) + (d x -1) + (e x -3) + (f x -2) + (g x 1) + (h x 3) + (i x 2) + (j x -1) + (k x -2) =  Result is a multiple of 7 then the full number is divisible by 7

5221244 – (4 x 1) + (4 x 3) + (2 x 2) + (1 x -1) + (2 x -3) + (2 x -2) + (5 x 1)4 +12 +4 –16 – 4 + 5=  14  which is  a multiple of 7 hence the nunmber is divisible by 7.

Another easier  way for finding divisibility by 7 is as follows:

Step 1: Separate the last  digit of the number ( for ex. number is 5495, then 2 parts are 549 and 5)

Step 2: Multiple the last digit by 2 ( 2 * 5 = 10)

Step 3: Subtract the number ( In our example , 549 -10 = 539) Repeat the step again till you get last number if it is divisible by 7 then the original number is also divisible by 7, the remaining steps in our case is ( 53 & 9,  multiply 9 * 2 = 18, subtract 53 -18 = 35 . 35 is divisible by 7) Hence the number 5495 is also divisible by 7

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Finding out if the number is easily divisible by 7 or not

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The other articles on the divisibility are as follows

  1. Divisibility by 4 or 8
  2. Divisibility by 3, 6 or 9, shortcut to check if the number is divisible by 3, 6 or 9
  3. Divisibility for prime numbers

 

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