Science, Maths & Technology

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# 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

1. Which of these numbers are multiples of 2?
2. Which of these numbers are multiples of 3?
3. Which of these numbers are multiples of 5?
4. Which of these numbers are multiples of 10?

1. 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
2. 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
3. 30, 45 and 80 are multiples of 5.
• 5 × 6 = 30
• 5 × 9 = 45
• 5 × 16 = 80
4. 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: 12 (meaning 1 × 1), 22 (meaning 2 × 2), 32 (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?

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