Division Tricks
Divisibility by 8 – Check the Last Three Digits
Like the trick for 4, but one place further: look at the last three digits.
This page explains the rule, shows why it works, and walks through worked examples. Then you can try it yourself and check your understanding with practice questions. Use the previous and next links at the bottom to move through the tricks in order.
The rule
The Rule: If the last three digits of a number are divisible by 8, the whole number is divisible by 8.
Why it works
Why It Works: This is the same idea as the rule for 4, just carried one step further. A thousand happens to equal 8 × 125, so every full thousand hiding inside a number is already a clean multiple of 8 and can be safely ignored. That leaves only the last three digits to decide the answer.
Formal Proof (for advanced learners)
Write N = 1000a + b, where b is the three-digit number formed by N’s last three digits (0–999). Since 1000 = 8·125, we have 1000a ≡ 0 (mod 8), so N ≡ b (mod 8). Hence N is divisible by 8 exactly when its last three digits are.
Examples
- 1000 → last three digits 000, divisible by 8.
- 3128 → last three digits 128 (128 ÷ 8 = 16), divisible by 8.
- 1234 → last three digits 234, not divisible by 8.
Step by step
Example A: is 9216 divisible by 8?
- Look at the last three digits of 9216: they make 216.
- 216 ÷ 8 = 27.
- So 9216 is divisible by 8.
Example B: is 5124 divisible by 8?
- Look at the last three digits of 5124: they make 124.
- 124 ÷ 8 = 15 remainder 4, so 8 does not go in exactly.
- So 5124 is not divisible by 8.
Try it yourself
Now it is your turn. A new random question appears each time. Choose True or False. If you are right, we show how the trick got you there, step by step. If you are not, you will see the full working two ways, the shortcut and the usual method, so you can spot exactly where your answer differed. Press New Question as often as you like: a few quick rounds is the best way to make the trick feel automatic.
Practice questions
Have a go on paper first, then tap Show answer to check your method.
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Is 64 divisible by 8?
Show answer
Yes. Look at the last three digits of 64: they make 64. 64 ÷ 8 = 8. So 64 is divisible by 8.
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Is 250 divisible by 8?
Show answer
No. Look at the last three digits of 250: they make 250. 250 ÷ 8 = 31 remainder 2, so 8 does not go in exactly. So 250 is not divisible by 8.
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Is 1200 divisible by 8?
Show answer
Yes. Look at the last three digits of 1200: they make 200. 200 ÷ 8 = 25. So 1200 is divisible by 8.
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Is 3132 divisible by 8?
Show answer
No. Look at the last three digits of 3132: they make 132. 132 ÷ 8 = 16 remainder 4, so 8 does not go in exactly. So 3132 is not divisible by 8.
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Can 45016 tickets be shared equally among 8 classes with none left over?
Show answer
Yes. Look at the last three digits of 45016: they make 16. 16 ÷ 8 = 2. So 45016 is divisible by 8.
Tips and watch-outs
- It works because 1000 = 8 × 125, so everything before the last three digits is automatically a multiple of 8.
- For a number below 1000, just check the whole number: is it in the 8 times table?