# Multiples and square numbers

When dealing with multiplication, it is important to know the meaning of multiples and square numbers.

## Multiples

A multiple of a number can be divided exactly by that number. So for example, 12 is a multiple of 2, 3, 4 and 6, because:

2 × 6 = 12

4 × 3 = 12

### Activity 9: Looking for multiples

Look at the following row of numbers, and then answer the questions below.

12, 17, 24, 30, 39, 45, 52, 80

- Which of these numbers are multiples of 2?
- Which of these numbers are multiples of 3?
- Which of these numbers are multiples of 5?
- Which of these numbers are multiples of 10?

#### Answer

- 12, 24, 30, 52 and 80 are multiples of 2.
- 2 × 6 = 12
- 2 × 12 = 24
- 2 × 15 = 30
- 2 × 26 = 52
- 2 × 40 = 80

- 12, 24, 30, 39 and 45 are multiples of 3.
- 3 × 4 = 12
- 3 × 8 = 24
- 3 × 10 = 30
- 3 × 13 = 39
- 3 × 15 = 45

- 30, 45 and 80 are multiples of 5.
- 5 × 6 = 30
- 5 × 9 = 45
- 5 × 16 = 80

- 30 and 80 are multiples of 10.
- 10 × 3 = 30
- 10 × 8 = 80

## Square numbers

A square number is made when you multiply any whole number by itself. For example:

1 × 1 = 1

2 × 2 = 4

3 × 3 = 9

**Hint:** Square numbers are commonly shown as: 1^{2} (meaning 1 × 1), 2^{2} (meaning 2 × 2), 3^{2} (meaning 3 × 3), etc.

### Activity 10: Identifying square numbers

You have been given the square numbers up to 3. Following the pattern, what are the square numbers from 4 to 12?

#### Answer

The answers are as follows:

4 × 4 = 16

5 × 5 = 25

6 × 6 = 36

7 × 7 = 49

8 × 8 = 64

9 × 9 = 81

10 × 10 = 100

11 × 11 = 121

12 × 12 = 144