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Greatest Common Factor (GCF) - Also known as Greatest Common Divisor (GCD)

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!