Year 8 Interactive Maths - Second Edition

## Factors

A factor of a given number is a whole number that divides exactly into the given number.

So, 4 is a factor of 12 as it divides exactly into 12, and 3 is also a factor of 12.

###### Note:

If a number can be expressed as a product of two whole numbers, then the whole numbers are called factors of that number.

So, the factors of 12 are 1, 2, 3, 4, 6 and 12.

### Common Factors

Common factors are factors that are common to two or more numbers.

#### Example 16

Find the common factors of 10 and 20.

##### Solution:

So, the common factors of 10 and 20 are 1, 2, 5 and 10.

#### Example 17

Find the common factors of 22 and 33.

##### Solution:

So, the common factors of 22 and 33 are 1 and 11.

### Highest Common Factor

The highest common factor (HCF) of two (or more) numbers is the largest common factor.

So, the common factors of 8 and 12 are 1, 2 and 4; and 4 is the largest common factor.

###### Setting out:

Often, we set out the solution as follows:

#### Example 18

Find the highest common factor of 16 and 32.