Question

What is the GCF of `45,80,75`?

Answer 1

`GCF=5`

Explanation:

`45=5times9`

`80=5times16`

`75=5times15`

Hence `GCF=5`

Answer 2

`5`
Found using the product of prime factors.

Explanation:

In most cases we should be able to find the GCF fairly easily by just knowing the multiplication tables up to 12 x 12. Sometimes a bigger number might be included which we do not know well.

It is good to have a method available for cases when we cannot find the GCF by inspection.

In order to find the GCF (and the LCM) write each number as the product of its prime factors.

`color(white)(xxxx) 45 = color(white)(xxxxxxxxxxx) 3xx3xx5`
`color(white)(xxxx) 80 = 2xx2xx2xx2color(white)(xx.xxx)xx5`
`color(white)(xxxx)75 = color(white)(xxxxxxxxxxxxxx)3xx5xx5`

`GCF =color(white)(xxxxxxxxxxxxxxxxxxx)5`

From this it is very clear that the only common factor is 5.

If we needed the LCM it can be calculated easily form this format:
Include each column pf factors, do not count factors that are in the same column twice.

`LCM = 2xx2xx2xx2xx3xx3xx5xx5 = 2^4 xx 3^2 xx 5^2 = 3600`