Numbers and sequences
Prime & composite numbers
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors.
How to tell them apart
1. Find the factors of the number (what divides into it exactly). 2. Exactly two factors → prime (e.g. 2, 3, 5, 7, 11). 3. More than two factors → composite (e.g. 4, 6, 9, 15). (1 is neither prime nor composite.)
Worked examples
A prime number
- Is 7 prime?
- The only factors of 7 are 1 and 7 — exactly two.
Answer: Yes, 7 is prime.
A composite number
- Is 9 prime?
- 9 has factors 1, 3 and 9 — that is more than two.
Answer: No, 9 is composite (not prime).
Where you see this in real life
- Prime numbers help keep credit-card numbers safe online.
- Working out if a number of objects can be shared into equal groups.
- Spotting numbers that only make one shape of rectangle.
Key words
- Prime number
- A number with exactly two factors: 1 and itself.
- Composite number
- A number with more than two factors.
- Factor
- A whole number that divides exactly into another number.