How to tell if a number is divisible by 8

The textbook rule for 8 is the last three digits, which on a four-digit number leaves you asking almost the same question you started with. Halving is the one a child can actually run.

How to check it

1. Halve the number. If it is odd, halving it leaves a half rather than a whole number, so stop: it does not divide by 8.
2. Halve the result. Stop if it turns odd.
3. Halve once more. If all three halvings landed on whole numbers, the number divides by 8.

Worked examples

The other way: the last three digits

Every thousand is 8 × 125, so thousands and everything above them are already whole numbers of 8s. Only the last three digits can decide the question.

For 109 816, look at 816: it is 8 × 102, so the whole number divides by 8.

This is the rule most textbooks print, and it is genuinely useful on long numbers. On a four-digit number it only removes one digit, and you are left asking whether 620 is a multiple of 8, which is no easier than the original question. That is why halving is the better first method.

Why halving three times works

8 = 2 × 2 × 2. Dividing by 8 is the same as dividing by 2 three times over, so if every one of those halvings lands on a whole number, the original divided by 8.

It also stops early and tells you why: the moment a halving turns odd, you know there were not enough 2s inside the number.

Where it goes wrong

• Halving twice and calling it done. Two halvings test 4, not 8.
• Rounding a half. 1155 ÷ 2 is 577.5, not 577, and a half means the answer is no. Getting stuck is the answer, not an inconvenience.
• Assuming an even number divides by 8. Only one even number in four does.

Questions people ask

Related rules

• How to tell if a number is divisible by 4
• How to tell if a number is divisible by 2