# Tests for Divisibility of Numbers - Divisibility by 3

## Notes

### Divisibility by 3:

First sum all the digits of the number, now check whether the result is divisible by 3. If the answer is divisible by 3, clearly the number will be divisible by 3.

### For example:

Consider the number 502.
Take sum of the digits (i.e. 5 + 0 + 2 = 7). Now check whether the sum is divisible by 3 or not.

If the sum is a multiple of 3 then the original number is also divisible by 3. Here, since 7 is not divisible by 3, 502 is also not divisible by 3.

Similarly, 636 is divisible by 3 completely as the sum of its digits i.e. 6 + 3 + 6 = 15, is a multiple of 3.

Now, let us consider the number 3576.

As above, we get

3576 = 3 × 999 + 5 × 99 + 7 × 9 + (3 + 5 + 7 + 6)

(3 + 5 + 7 + 6) i.e., 21 which is divisible by 3,

Therefore, 3576 is divisible by 3.

### Let us explain divisible by 3 rule:

If the number is 'cba', then, 100c + 10b + a = 99c + 9b + (a + b + c)

= ubrace(9(11c + b))_("divisible by 3") + (a + b + c)

Hence, divisibility by 3 is possible if a + b + c is divisible by 3.

## Example

Check the divisibility of 2146587 by 3.

The sum of the digits of 2146587 is 2 + 1 + 4 + 6 + 5 + 8 + 7 = 33.
This number is divisible by 3 (for 33 ÷ 3 = 11).
We conclude that 2146587 is divisible by 3.

## Example

Check the divisibility of 15287 by 3.

The sum of the digits of 15287 is 1 + 5 + 2 + 8 + 7 = 23.
This number is not divisible by 3.
We conclude that 15287 too is not divisible by 3.
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