The end of a number decides
A baker packs 3,624 laddus into boxes of 8. Will every box be full?
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- 3,624 is 3,000 + 624.
- 3,000 is 8 × 375. It is a multiple of 8.
- Only the last three digits, 624, can change the answer.
- 624 ÷ 8 = 78. So 3,624 divides by 8.
The rule
Yes. 3,624 ÷ 8 = 453, so every box is full.
Each place is worth 1, 10, 100, 1,000 and so on. Places from 10 up are multiples of 2, 5 and 10. From 100 up, each is a multiple of 4. From 1,000 up, each is a multiple of 8. So places left of the end digits add no remainder. Only the end of a number can change the answer.
Rule: For 2, 5 or 10, look at the last digit. For 4, look at the last two digits. For 8, look at the last three.
| Test | Look at | It passes when |
|---|---|---|
| 2 | last digit | it is 0, 2, 4, 6 or 8 |
| 5 | last digit | it is 0 or 5 |
| 10 | last digit | it is 0 |
| 4 | last two digits | they make a multiple of 4 |
| 8 | last three digits | they make a multiple of 8 |
Take 5,716. It ends in 6, so it divides by 2. Its last two digits are 16, a multiple of 4. So it divides by 4. Its last three digits are 716, and 716 ÷ 8 leaves remainder 4. So 5,716 does not divide by 8.
Watch out!
An even number need not divide by 4. 22 is even, and 22 ÷ 4 leaves 2.