Question

What is the greatest common factor of 60 and 72?

Answer 1

12

Explanation:

I like to answer these questions by first doing prime factorizations:

`60=2xx30=2xx2xx15=2xx2xx3xx5`
`72=2xx36=2xx2xx18=2xx2xx2xx9=2xx2xx2xx3xx3`

The GCF will have all the numbers that are common to both 60 and 72.

`GCF=?`

Let's start with 2's first. 60 has two 2s, while 72 has three. Two 2s are common to both, so our GCF will have two 2s:

`GCF=2xx2xx?`

Now 3s. 60 has one 3 and 72 has two 3s. One 3 is common to both, so we'll put that in:

`GCF=2xx2xx3xx?`

And lastly to 5s - 60 has one but 72 doesn't, so there's nothing common there. And so we stop here:

`GCF=2xx2xx3=12`

`60=12xx5`
`72=12xx6`

Answer 2

12

Explanation:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. The common factors of both numbers are 1, 2, 3, 4, 6, and 12. Which means that 12 is the greatest common factors.