Factors first
A factor is a whole number that divides another number exactly, with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. Counting factors helps us sort numbers into prime and composite.
Key idea
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite.
Worked example
Worked example
Is 12 prime or composite?
Factors of 12: 1, 2, 3, 4, 6, 12 — that is six factors.
More than two factors, so 12 is composite.
A special prime
The smallest prime number is 2, and it is the only even prime number. Every other even number can be divided by 2, so it has an extra factor and is composite. To test a small number, try dividing it by 2, 3 and 5. If none of them divide it exactly, the number is usually prime. For example, 7 cannot be divided evenly by 2, 3 or 5, so 7 is prime. The first few prime numbers are 2, 3, 5, 7, 11 and 13.
Remember
- Prime = exactly 2 factors.
- Composite = more than 2 factors.
- 1 is neither; 2 is the only even prime.
- Test by dividing by 2, 3 and 5.