# 1.02 Factors and multiples

Lesson

## Ideas

Many number problems we work on can be made easier by knowing the factors of a number. Do you remember how to find the factors for a number?

### Examples

#### Example 1

If we multiply 4 by 14, we get 56, so 4 and 14 make a factor pair of 56.

Which of the following options is also a factor pair of 56?

A
14 and 2
B
4 and 7
C
8 and 7
D
2 and 2
Worked Solution
Create a strategy

Multiply each pair of numbers together.

Apply the idea

Option A: \begin{array}{c} &&1&4 \\ &\times &&2\\ \hline &&2&8 \\ \hline \end{array}

Option B: 4\times7=28

Option C: 8\times7=56

Option D: 2\times2=4

Only the pair in option C multiplies to 56. The answer is option C.

Idea summary

All numbers have at least one factor pair, 1 and itself.

To check if a pair of numbers is a factor pair of a given number, multiply the pair of numbers together.

## Factors

Let's explore factors here, as well as learn about the highest common factor (HCF).

### Exploration

Drag the sliders to find multiples of numbers from 1 to 12.

The number sentence shows us multiples of the numbers on the left, and factors of the number on the right. e.g. 6\times 8=48 means that 6 and 8 are factors of 48, and that 48 is a multiple of 6 and of 8.

### Examples

#### Example 2

Which of these numbers is 6 a factor of?

A
30
B
32
C
17
D
39
Worked Solution
Create a strategy

Write down the multiples of 6.

Apply the idea

The first 7 multiples of 6 are: 6,\, 12,\, 18,\, 24,\, 30,\, 36,\, 42.

Out of all the options only 30 is in the above list.

The correct answer is Option A.

Idea summary

The highest common factor of two numbers is the highest number that is a factor of both numbers.

## Multiples

We've looked at factors, so it's time to look at multiples and find out what a lowest common multiple (LCM) is.

### Examples

#### Example 3

True or False: 18 is a multiple of 3.

Worked Solution
Create a strategy

Write down the factors of 18.

Apply the idea

The factors of 18 are: 1,2,3,6,9,18.

Since 3 is a factor of 18, then 18 is a multiple of 3. This means the statement is true.

Idea summary

Factors and multiples are related to multiplication facts. Writing out a multiplication problem, such as 4\times 6=24 can help us remember which is which.

The lowest common multiple of two numbers is the lowest number that is a multiple of both numbers.