How do you find the gcf of #16a^2 - 64b#?
Note: I think what you're referring to is the GCF of the coefficients, which you would factor out of the equation. If this isn't what you're talking about, sorry this explanation won't help.
You want to look at the coefficients, 16 and 64 and look at what factors they share. The factors of 16 are 1, 16, 2, 8, and 4. The factors of 64 are 1, 64, 2, 32, 4, 16, and 8. While it can be tedious to list out all the factors, it is a trustworthy method. As you can see from the lists above, 16 itself is the greatest factor that is common between the 2 lists.
Therefore, your factoring would look like this: