What is a factor?
A factor of a number divides into it evenly (no remainder).
Factors of 12: 1, 2, 3, 4, 6, 12
We can organise factors into pairs that multiply to give the number:
| Pair | Product |
|---|---|
| 1 × 12 | 12 |
| 2 × 6 | 12 |
| 3 × 4 | 12 |
So 12 has 6 factors.
Factor pairs of 12
What is a multiple?
A multiple of a number is what you get when you multiply it by 1, 2, 3, 4, …
Multiples of 7: 7, 14, 21, 28, 35, 42, …
Multiples go on forever — there’s no “last” multiple.
Quick check: Is 56 a multiple of 7? Yes, because 7 × 8 = 56.
Prime vs composite
- A prime number has exactly 2 factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13
- A composite number has more than 2 factors. Examples: 4, 6, 8, 9, 10, 12
- The number 1 is neither prime nor composite — it has only 1 factor.
Start with 1
Try 2
Try 3
Try 4
To find all factors: start from 1 and work up. Stop when the pairs start repeating.
How to test if a number is prime
Try dividing by small primes (2, 3, 5, 7, …). If none divide evenly, it’s prime.
Is 29 prime?
- 29 ÷ 2 = 14 r 1 (not even)
- 29 ÷ 3 = 9 r 2 (nope)
- 29 ÷ 5 = 5 r 4 (nope)
- 5 × 5 = 25 < 29, but 6 × 6 = 36 > 29, so we can stop.
- 29 is prime.
Practice
Which of the following is NOT a factor of 24?
24 ÷ 5 = 4 remainder 4. Since it doesn't divide evenly, 5 is not a factor of 24.
How many factors does 18 have? (List them in your head: 1, 2, 3, …)
Factors of 18: 1, 2, 3, 6, 9, 18 — that's 6 factors.
Which number is prime?
23 has only two factors: 1 and 23. The others are composite (15 = 3×5, 21 = 3×7, 27 = 3×9).
What is the 5th multiple of 9?
Multiples of 9: 9, 18, 27, 36, 45. The 5th multiple is 45.
Which statement is true about the number 1?
1 has only one factor (itself), so it doesn't meet the definition of prime (exactly 2 factors) or composite (more than 2).
Challenge
Quick-Fire Round