A common factor must divide every given integer. In prime factorisations, it can use only primes present in all the numbers, each to no more than the smallest available power. Taking all these powers gives the highest common factor (HCF). Example 84=22 x 3 x 7, and 126=2 x 32 x 7. HCF(84,126)=2 x 3 x 7=42. To make the greatest possible number of identical packs from 84 pencils and 126 erasers with none left, make 42 packs. Each contains 2 pencils and 3 erasers. If no prime is common to all the integers, the HCF is 1, not 0.

A common factor must divide every given integer. In prime factorisations, it can use only primes present in all the numbers, each to no more than the smallest available power. Taking all these powers gives the highest common factor (HCF).

\(84=2^2\times3\times7\), and \(126=2\times3^2\times7\).

\(\operatorname{HCF}(84,126)=2\times3\times7=42\).

To make the greatest possible number of identical packs from \(84\) pencils and \(126\) erasers with none left, make \(42\) packs. Each contains \(2\) pencils and \(3\) erasers.

If no prime is common to all the integers, the HCF is \(1\), not \(0\).

Highest common factor

Highest common factor