Question 77423
We can see the GCF among the numbers is the greatest number that can go into 12,18,and 6. This number is 6 since it can go into all 3 of these numbers. Now we need to look at the variables. We see that they all have a and b in their terms, so our GCF will have at least one of each. Since the lowest exponent for a is 2, our GCF for a is {{{a^2}}}. Since the lowest exponent for b is 2, the GCF for b is {{{b^2}}}. Combining all of this info, we get:

GCF:
{{{6a^2b^2}}}

Notice how we can factor out the GCF out of all of these evenly. For instance, say we have


{{{12a^3b^2+18a^2b^3+6a^4b^4}}}

We can factor the GCF out of the expression to get

{{{6a^2b^2(2a+3b+a^2b^2)}}}

When we distribute {{{6a^2b^2}}} to the terms in the parenthesis we get 
{{{12a^3b^2+18a^2b^3+6a^4b^4}}} again