# What is the greatest common factor of 180 and 225?

##### 1 Answer

Feb 3, 2017

45

#### Explanation:

Let's do a prime factorization of the two numbers:

And now let's find what's in the GCF by seeing what is common to both:

**2**

There are 2s in 180 but not 225, so there are no 2's in the GCF.

**3**

There are two 3s in both 180 and 225, and so the GCF has two 3s.

**5**

There is one 5 in 180 and two in 225, and so the GCF has one 5.

And now let's put it all together: