Question

What is the greatest common factor of 21 and 63?

Answer 1

`HCF(21,63)=gcd(a,b)=21`

Explanation:

By definition, `a` is a factor of `b` if it can divide perfectly into `b` without leaving a remainder.

That is, `a|biff EEk in ZZ` such that `a/b=k or a=kb`.

So hence we may list all the factors of each number and see which are common to both sets and then select the highest one that is common.

Factors of `21={1,3,7,21}`

Factors of `63={1,3,7,9,21,63}`

`therefore`the highest common factor (HCF) is `21`.

Note: Some texts also refer to this as the greatest common divisor (gcd), and if the numbers are very big, we may use Euclid's Algorithm to find it.

Answer 2

`21`

Explanation:

Both `21` and `63 = 3 * 21` are divisible by `21` and `21` has no greater factor, so this must be the greatest common factor.