Question

Can someone explain to me how to find the GCF?

Answer 1

See below for an idea:

Explanation:

The GCF (Greatest Common Factor) can be found by first factoring down to primes of the numbers in question. Let's do this for the numbers 6, 9, and 15:

`6=2xx3`
`9=3xx3`
`15=3xx5`

Now we find what is common to all the numbers.

The 6 has a 2 and a 3.
The 9 has two 3s
The 15 has a 3 and a 5.

The only number that is common to all of them is a single 3, and so that is the GCF.

If I wanted to find the GCF of those three numbers and also the number 4, we'd have:

`4=2xx2`
`6=2xx3`
`9=3xx3`
`15=3xx5`

Since the 4 doesn't have 3 as a factor, there is no factor that we've listed that is common to all four of them, and so the GCF is 1 (1 is a factor of all numbers).

Answer 2

See below:

Explanation:

Find the Greatest Common Factor of numbers by listing their prime numbers. Here are some example problems:

• What is the GCF of 9 and 12?

List their prime factors:

`9= 3 xx3`
`12 =3 xx 2 xx 2`

Now highlight all of the terms that they have in common:

`9= color(red)3 xx3`
`12 =color(red)3 xx 2 xx 2`

They only share a `3`, so their GCF is `3`.

• What is the GCF of 12 and 18?

List their prime factors and highlight their common terms:

`12 = color(red)3 xx color(blue)2 xx 2`
`18 = color(red)3 xx 3 xx color(blue)2`

Since they have `3` and `2` in common, multiply them together:

`3 xx 2 = 6`

The GCF is `6`.

• What is the GCF of 9, 18, and 27?

List their prime factors and highlight the common terms:

`9 = color(red)3 xx color(blue)3`
`18 = color(red)3 xx color(blue)3 xx 2`
`27 = color(red)3 xx color(blue)3 xx 3`

Multiply these two terms together:

`3 xx 3 = 9`

The GCF is 9.