Supercharge your learning!

Use adaptive quiz-based learning to study this topic faster and more effectively.

Highest common factor

A common factor is a factor that two numbers share.

$$4$$ is a common factor of $$8$$ and $$12$$.

$$6$$ is not a common factor of $$18$$ and $$15$$.

Two integers have a unique highest common factor (HCF). It is also known as their greatest common divisor (GCD).

The factors of $$35$$ are $$1$$, $$\Tred{5}$$, $$7$$ and $$35$$. The factors of $$15$$ are $$1$$, $$3$$ , $$\Tred{5}$$ and $$15$$. So the highest common factor of $$15$$ and $$35$$ is $$\Tred{5}$$.

The common factors of $$100$$ and $$70$$ are $$1$$, $$2$$, $$5$$ and $$\Tred{10}$$. So $$\HCF(100,70) = \Tred{10}$$.

It is possible for the highest common factor of two numbers to be $$1$$ or one of the numbers.

$$$ \HCF(20, 9) = \Tred{1},\quad \HCF(6,9) = \Tred{3},\quad\HCF(6,18) = \Tred{6}. $$$