A **common factor** is a factor that is shared by two or more numbers. For example, a common factor of 8 and 10 is 2, as 2 is a factor of 8, and 2 is also a factor of 10.

The **highest common factor (HCF)** is found by identifying all common factors of two numbers and selecting the largest one.

For example, 8 and 12 have common factors of 1, 2 and 4. The highest common factor is 4.

- Question
Find the highest common factor of 9 and 21.

Start by listing the factors of 9 and 21:

**factors of 9**: 1, 3, 9**factors of 21**: 1, 3, 7, 21

The common factors of 9 and 21 are 1 and 3, so the highest common factor of 9 and 21 is 3.

A **common multiple** is a number that is a shared multiple of two or more numbers. For example, 24 is a common multiple of 8 and 12, as 24 is in the 8 times tables ( ) and 24 is in the 12 times tables ( ).

The **lowest common multiple (LCM)** is found by listing multiples of each number and circling any common multiples. The lowest one is the lowest common multiple.

- Question
Find the lowest common multiple of 5 and 6.

List the multiples of 5 and 6:

**multiples of 5**: 5, 10, 15, 20, 25,**30**, 35...**multiples of 6**: 6, 12, 18, 24,**30**...

The lowest common multiple of 5 and 6 is 30, as it is the first multiple found in both lists.