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# 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.

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