Question

What is the GCF of 36 and 60?

Answer 1

Greatest Common Factor is `12`.

Explanation:

Factors of `36` are `{1,2,3,4,6,9,12,18,36}`.

Factors of `60` are `{1,2,3,4,5,6,10,12,15,20,30,60}`.

Common factors are `}1,2,3,4,6,12}`.

Hence Greatest Common Factor is `12`.

Answer 2

`HCF = 2xx2xx3 = 12`

Explanation:

A method of finding GCF and LCM - especially of several numbers if they are larger than usual - is to write the numbers as the product of the prime factors.

In this way we can immediately see which factors are common:

`color(white)(xxxxxx)36 = color(red)(2xx2xx3)xx3`
`color(white)(xxxxxx)60= color(red)(2xx2xx3)color(white)(xxx)xx5`

`GCF=color(white)(xx) = color(red)(2xx2xx3) color(white)(xxxxx) = 12`

`LCM=color(white)(xx) = 2xx2xx3xx3xx5 color(white)(xxxxx) = 180`

If you have any number written as the product of its prime factors, then you know everything there is to know about that number.