Factors, multiples, and primes

Step 6 · Long division and equivalent fractions topics

Find all the factor pairs of a number up to 100, list its multiples, and tell whether it is prime or composite.

Factor pairs

A factor of a number divides into it exactly, with no remainder. Factors come in pairs that multiply to the number: 3 × 4 = 12, so 3 and 4 are a factor pair of 12.

Factor pair	Product
1 × 12	12
2 × 6	12
3 × 4	12

The factor pairs of 12: 1 and 12, 2 and 6, 3 and 4.

Each pair is a way to set out 12 squares in a full rectangle: 1 by 12, 2 by 6 or 3 by 4.

Example: Finding every pair

List the factors of 36.

Try 1, 2, 3 and so on: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
5 does not go into 36, and after 6 the pairs start to repeat.

Answer1, 2, 3, 4, 6, 9, 12, 18, 36

Multiples

The multiples of a number are what you get when you count by it: the multiples of 6 are 6, 12, 18, 24, 30, and so on for ever.

Factors and multiples are two sides of the same fact. 6 × 4 = 24 says that 6 is a factor of 24, and that 24 is a multiple of 6.

Prime or composite

A prime number has exactly two factors: 1 and itself. 7 is prime, because only 1 × 7 makes 7. A composite number has more than two factors: 8 is composite, because 2 × 4 = 8 too.

7 squares make only one rectangle, 1 by 7: 7 is prime.

The primes up to 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. The number 1 is neither prime nor composite: it has only one factor.

Example: Prime or composite?

Is 51 prime?

The digits add up to 5 + 1 = 6, a multiple of 3, so 3 is a factor.
51 = 3 × 17.

AnswerNo. 51 is composite.

Try it yourself

Work each one on paper first, then open the answer to check.

List all the factor pairs of 20.
Show answer
1 × 20, 2 × 10, 4 × 5.
Is 7 a factor of 42?
Show answer
Yes. 7 × 6 = 42.
Write the first five multiples of 8.
Show answer
8, 16, 24, 32, 40.
Is 29 prime or composite?
Show answer
Prime. Its only factors are 1 and 29.
Is 57 prime or composite?
Show answer
Composite. 57 = 3 × 19.