Arithmetic/Highest Common Factor

The highest common factor (HCF) or greatest common divisor (GCD) can be found in a similar fashion. In this case, the product of the prime factors common to all the numbers gives the HCF.

For example, if we wish to find the HCF of 60, 12 and 102 we write

$$ \begin{matrix} 60=2^2 \cdot 3 \cdot 5 \\ 12=2^2 \cdot 3 \\ 102=2 \cdot 3 \cdot 17 \end{matrix} $$

Now the HCF is $$2 \cdot 3=6$$.

Two numbers which have an HCF of 1, for example 12 and 5, are said to be coprime - they have no factors in common (except 1).