Depending on what level you are at, there are some more advanced methods for finding the GCF. This first one is probably at the pre-algebra level and the others may not be.
The Prime Factorization Method:
Let's just do one that we did the other way and I'll walk you through it:
|List the prime factorization of each using exponents:
|Take the SMALLER of each of the exponents...
|Multiply these together to get the answer:
Is this what we got the other way?