## Divisibility Test by 2- Rules

We can use the rule of **test** **for** **divisibility ****by 2 **to find out the divisibility of given number by 2. There are rules of finding out whether the number is divisible by 2 or not.

We have seen that all multiples of-

- 3 are divisible by 3.
- 4 are divisible by 4.
- 5 are divisible by 5
- 6 are divisible by 6
- 9 are divisible by 9
- 10 are divisible by 10

First rule is- all multiples of a number are divisible by that number.

So all multiples of 2 that is 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26… are

divisible by 2.

We know what even and odd numbers are.

All even numbers are divisible by 2. We know that all even numbers have 0,2,4,6 or 8 at their unit place. And obviously, all odd numbers that is numbers having 1,3,5,7 or 9 at their unit place are not divisible by 2.

If we actually divide-

- even number by 2, we get the remainder 0. It means, this number is completely divisible by 2.
- odd number by 2, we get the remainder other than 0. It means, this number is not divisible by 2.

### So we have test for divisibility by 2 as;

All –

- multiples of 2
- even numbers

are divisible by 2.

We shall take some examples.

Which of the numbers 602, 834, 5670, 3786, 4029, 3875 are **divisible by 2**?

Of the given numbers, 602, 834, 5670, 3786, 4029, 3875 have the numbers 2, 4, 0 and 6 at the units place. Therefore these numbers are divisible by 2. If we actually divide these numbers by 2 we get remainder 0. But the numbers 4029 and 3875 do not have any 0, 2, 4, 6 or 8 at the units place. Therefore these numbers are **not divisible by 2.**

### Example- 1

**34,726**

In the number thirty four thousand seven hundred and twenty six, the last digit is 6. That is 6 is at unit place of this number. So this is an even number and we know that all even numbers are divisible by 2. Hence 34,726 is divisible by 2.

### Example- 2

**34,267**

In the number thirty four thousand two hundred and sixty seven, the last digit is 7. That is 7 is at unit place of this number. So this is an odd number and we know that all odd numbers are not divisible by 2. Hence 34,267 is not divisible by 2.

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