Divisibility by 4

A number is divisible by 4 if its last two digits form a number divisible by 4 (00 counts too).

Examples

Why it works

100 = 4 × 25, so any number of hundreds is divisible by 4. Split off the hundreds, and only the last two digits are left to check:

916 = 900 ✓ + 16 ✓ → divisible by 4
918 = 900 ✓ + 18 ✗ → not divisible by 4

This uses the rule for the divisibility of a sum.

Quick check for the last two digits

Not sure whether an ending like 76 is divisible by 4? Look at its tens digit:

For example, 58 is not divisible by 4: its tens digit 5 is odd, and 8 is not 2 or 6.

Careful: don't look only at the last digit. 18 and 28 both end in 8, but only 28 is divisible by 4.
Every number divisible by 4 is even, but not every even number is divisible by 4: 22, 918 and 1,230 are even, but not divisible by 4. See divisibility by 2.

Try it yourself

Click a question to see the answer.

1. Which of these numbers are divisible by 4: 312, 1,418, 7,000, 5,564, 9,090?

312, 7,000 and 5,564 – they end in 12, 00 and 64.

2. Is 123,456 divisible by 4?

It ends in 56, and 56 = 4 × 14. Yes

3. Which digits can go in the box so that 5,32 is divisible by 4?

The last digit is 2, so the tens digit must be odd: 1, 3, 5, 7 or 9.

4. Which digits can go in the box so that 7,21 is divisible by 4?

The tens digit 1 is odd, so the last digit must be 2 or 6: 7,212 and 7,216.

5. True or false: every number that ends in 4 is divisible by 4.

False. 14 ÷ 4 = 3 R 2. The tens digit of 14 is odd, so the last digit would have to be 2 or 6.

6. What is the largest three-digit number divisible by 4?

996, because 96 = 4 × 24. 999, 998 and 997 end in 99, 98 and 97, which are not divisible by 4.