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

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:

$6 = 2 \times 3$
$9 = 3 \times 3$
$15 = 3 \times 5$

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:

$4 = 2 \times 2$
$6 = 2 \times 3$
$9 = 3 \times 3$
$15 = 3 \times 5$

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).

Jun 7, 2018

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:

$9 = 3 \times 3$
$12 = 3 \times 2 \times 2$

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

$9 = \textcolor{red}{3} \times 3$
$12 = \textcolor{red}{3} \times 2 \times 2$

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:

$12 = \textcolor{red}{3} \times \textcolor{b l u e}{2} \times 2$
$18 = \textcolor{red}{3} \times 3 \times \textcolor{b l u e}{2}$

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

$3 \times 2 = 6$

The GCF is $6$.

• What is the GCF of 9, 18, and 27?

List their prime factors and highlight the common terms:

$9 = \textcolor{red}{3} \times \textcolor{b l u e}{3}$
$18 = \textcolor{red}{3} \times \textcolor{b l u e}{3} \times 2$
$27 = \textcolor{red}{3} \times \textcolor{b l u e}{3} \times 3$

Multiply these two terms together:

$3 \times 3 = 9$

The GCF is 9.