What’s the difference?
| Meaning | Example for 12 | |
|---|---|---|
| Factor | divides into the number exactly (no remainder) | 1, 2, 3, 4, 6, 12 |
| Multiple | an answer in the number’s times table | 12, 24, 36, 48, … |
Memory hook: factors are few and fit inside the number. Multiples are many and go on for ever.
Finding factors in pairs
Work up from 1 and write each pair that multiplies to make the number:
- 12 = 1 × 12 = 2 × 6 = 3 × 4
- So the factors of 12 are 1, 2, 3, 4, 6, 12.
Stop when the pairs start repeating.
Common factors and common multiples
- Highest common factor (HCF): the biggest factor two numbers share. HCF of 12 and 18 is 6.
- Lowest common multiple (LCM): the smallest multiple two numbers share. LCM of 4 and 6 is 12.
Quick divisibility checks
| Divides by | If… |
|---|---|
| 2 | the number is even |
| 3 | the digits add up to a multiple of 3 (51 → 5 + 1 = 6 ✔) |
| 4 | the last two digits divide by 4 (316 → 16 ✔) |
| 5 | it ends in 0 or 5 |
| 9 | the digits add up to a multiple of 9 |
| 10 | it ends in 0 |
Watch out! 1 and the number itself are always factors, so don’t forget them. And every number is a multiple of itself.
👆 Factor finder
Tap all the factors of 24
🎮 Factor or multiple?Question 1 of 5