# Divisibility by 5

The number 10 is divisible by 5. Every number with 0 as a last digit is also divisible by 5, because we can represent it as a sum of tens.

For example: 40 is divisible by 5, because

40 = 10 + 10 + 10 + 10

As for a number with a different last digit, we can always represent it as a sum of a number with 0 as a last digit and the number of ones.

For example: 425 = 420 + 5

428 = 420 +8

The number 425 is divisible by 5 because the two addends (420 and 5) are both divisible by 5

The number 428 is not divisible by 5 because one of the addends (8) is not divisible by 5.

So, divisibility by 5 depends only on the last digit. If this digit is either 5 or 0, the number is divisible by 5.

**Divisibility by 5 - examples:**

The numbers 105, 275, 315, 420, 945, 760 can be divided by 5 evenly.

The numbers 151, 246, 879, 1404 are not evenly divisible by 5.

### A quick way to divide numbers by 5

*Example 1:*

Suppose you need to divide 342 by 5**342:5 = 68.4**

*First step:*

Multiply the number by 2.

342 x 2 = 684

*Second step:*

Move the decimal point one place to the left and you get 68.4

*Example 2:*

Divide 415 : 5 = ?

First step: 415 x 2 = 830

Second step: 83.0, and your answer is 83.

### A quick way to multiply by 5

Let's multiply quickly without a calculator 62 x 5 = ?

*First step:*

Divide 62 by 2 - 62:2 = 31

*Second step:*

Multiply the result by 10.

31 x 10 = 310

So 62 x 5 = 310

### Square two-digit numbers ending in 5

Example: 35^{2} = ?

*First step:*

Multiply the first digit by the next integer: 3 x 4 = 12

*Second step:*

Append 25 at the end

and your answer is 1225.