Factors, multiples, and prime numbers — introduction

Factors, multiples, and prime numbers — introduction

In Year 4 you start thinking about numbers in two new ways: what divides them (factors) and what they divide into (multiples). They are two sides of the same coin.

A quick example

Take the number 12.

  • The numbers that divide 12 exactly, with no remainder, are 1, 2, 3, 4, 6 and 12. These are the factors of 12.
  • The numbers you get by multiplying 12 by 1, 2, 3, … are 12, 24, 36, 48, 60, … These are the multiples of 12.

Same number, two different families.

Factors come in pairs

Whenever a number divides 12, you also know its "partner" — the matching factor that multiplies to 12.

PairProduct
1 × 1212
2 × 612
3 × 412

So 12 has six factors in total: 1, 2, 3, 4, 6, 12. Three pairs, six numbers.

Multiples go on forever

Multiples are easier. They are just the times-table answers.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, …

You can carry on as long as you like — the list never ends. Every multiple of 5 also ends in 5 or 0, which makes them quick to spot.

Prime and composite

If a number has exactly two factors — only 1 and itself — it's called a prime number. The first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, …

If a number has more than two factors (so it can be split as a product of smaller numbers), it's called composite. 12 is composite because it has six factors.

The number 1 is special — it has only one factor (itself), so it's neither prime nor composite.

What you'll learn

Try it out