Highest common factor (HCF)

We know Highest = Biggest number

Common = Anything the same

Factor = Take a number apart using ladders

The highest common factor is the highest number that similarly multiplies into 2 or more numbers

Common ground - Is there anything the same?

So logically

Highest common factor are:

The HCF is the highest common factor

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

Factorise 12 and 30 using the ladder method and take the factors forward
Take the multiples of 12 and 30 that are the same showing the HCF is 6

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
Factorise 12 and 15 using the ladder method and take the factors forward
Take the multiples of 12 and 15 only showing one meaning the HCF is 3

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
Factorise 60 and 72
The highest common factor here is 12

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
Factorise 36 54 and 72 using the ladder method
The highest common factor is 18

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.