# Highest common factor (HCF)

We know Highest = Biggest number

Common = Anything the same

Factor = Take a number apart using ladders

Common ground - Is there anything the same?

So logically

Highest common factor are:

**Example 1**

What is the highest common factor of the numbers 12 and 30?

Highest common factor = i. Take apart using ladders

ii. What have they in common

iii. Choose the biggest number

i. Take apart using ladders

ii. What they have in common

are 2, 3 and 6.

iii. The biggest number is 6.

**Answer:**

The highest common factor of 12 and 30 is 6.

**Example 2**

What is the highest common factor of the numbers 12 and 15?

Highest common factor = i. Take apart using ladders

ii. What have they in common

iii. Choose the biggest number

i. Take apart using ladders

ii. What they have in common

only 3.

iii. This makes 3 the biggest number too.

**Answer:**

The highest common factor of 12 and 15 is 3.

**Example 3**

What is the highest common factor of the numbers 60 and 72?

Highest common factor = i. Take apart using ladders

ii. What have they in common

iii. Choose the biggest number

i. Take apart using ladders

ii. What they have in common is

2, 3, 6 and 12.

iii. The biggest number is 12.

**Answer:**

The highest common factor of 60 and 72 is 12.

**Example 4**

What is the highest common factor of the numbers 36, 54 and 72?

Highest common factor = i. Take apart using ladders

ii. What have they in common

iii. Choose the biggest number

i. Take apart using ladders

ii. What they have in common is

2, 3, 6, 9 and 18.

iii. The biggest number is 18.

**Answer:**

The highest common factor of 36, 54 and 72 is 18.