Divisibility by 2

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

Numbers divisible by 2 are called even. All other whole numbers are odd: they end in 1, 3, 5, 7 or 9.

Even:  0, 2, 4, 6, 8, 10, 12, 14, 16, …
Odd:  1, 3, 5, 7, 9, 11, 13, 15, 17, …

0 is even, because 0 ÷ 2 = 0 with no remainder.

Examples

The other digits don't matter: 88,881 is full of 8s, but it ends in 1, so it is odd.

Why it works

Split the number into tens and ones: 596 = 590 + 6.
590 is 59 tens, and 10 = 2 × 5, so 590 is divisible by 2. Only the last digit is left to check:

596 = 590 ✓ + 6 ✓ → divisible by 2
597 = 590 ✓ + 7 ✗ → not divisible by 2

This uses the rule for the divisibility of a sum.

Careful: even does not mean divisible by 4. 918 ends in 8, so it is even, but 918 ÷ 4 = 229 R 2. See divisibility by 4.

Adding and multiplying even and odd numbers

Try it yourself

Click a question to see the answer.

1. Which of these numbers are even: 34, 57, 100, 2,461, 9,998?

34, 100 and 9,998 – they end in 4, 0 and 8.

2. What is the largest three-digit even number?

998. 999 ends in 9, so it is odd.

3. Is 0 even or odd?

Even, because 0 ÷ 2 = 0 with no remainder.

4. Without adding, is 347 + 285 even or odd?

Both numbers are odd, and odd + odd = even.
Even (347 + 285 = 632)

5. Without multiplying, is 25 × 37 even or odd?

Both numbers are odd, and odd × odd = odd.
Odd (25 × 37 = 925)

6. Use the digits 3, 4 and 7 once each. Write all the even three-digit numbers you can make.

An even number must end in 4, so the answer is 374 and 734.