Find the GCF of 4g^4 and 34g^3.

Yes, find the prime factors.

4 can be written as 2*2.

g^4 can be written as g*g*g*g.

That is the prime factorization of the first expression.

4g^4 can be written as 2*2*g*g*g*g.

34 can be written as 2*17.

And again we can split up the g business: g^3 is g*g*g.

34g^3 can be written as 2*17*g*g*g.

What do these expressions have in common?

They have a 2 in common,

and three of the g's in common, ya?

Therefore the GCF (4g^4, 34g^3) = 2g^3.