Divisibility Rules

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If you know the divisibility rules and right patterns of multiplying given numbers, you can definitely save your precious time. Especially in no calculator use sections, it can remarkably help you out when you are required to deal with larger numbers. Some of the simple divisibility rules are following.

  1. For the numbers 2, the multiples are always even.
  2. For the numbers 5, the multiples always end in either 5 or 0.
  3. For the number 10, the multiples always end in 0.

But if you come across a problem like this in your examination:

Find a, if b is a positive integer greater than 10 and ab = 57.

If you don’t instantly recognize the potential factors for 57, there is a 3-9 divisibility test. In order to check whether a number is divisible by 3 or 9, all you need to do is simply add up its digits in your mind and check if they add up to a smaller multiple of 3 or 9.

It will be divisible by both 3 and 9 if they add up to a multiple of 9. In case, they add up to a multiple of 3, then the number will be only divisible by 3. Have a look

For number 57: 5 + 7 = 12

12 is a multiple of 3 and it will be only divisible by 3 and not 9.

Now divide 57 by 3

57/3=19

As b is greater than 10, then b is 19, making a =3.

You can use the logic to check out a has to be 3 by doing the divisibility test.

In case, 57 didn’t pass the 3-9 divisibility test, chances are that it will probably a multiple of 7.

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