# Can someone explain to me how to find the GCF?

##### 2 Answers

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:

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:

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).

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

**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 xx 2 = 6#

The GCF is

**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.