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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:

Find  GCF( 24 , 36 )

 

1 )List the prime factorization of each using exponents:
24 = 2^3 x 3  ...  36 = 2^2 x 3^2  ...  Line up the bases
 
2 )Take the SMALLER of each of the exponents...
24 = 2^3 x 3^1
36 = 2^2 x 3^2
 
3 )Multiply these together to get the answer:

GCF( 24 , 36 ) = 2^2 x 3^1 = 12

Is this what we got the other way?

Yep!