The same idea is applied to polynomials. If we look at all of the coefficients to begin with (25,15,and 356) we would see that 5 could go into 25 and 15, but not into 356. Since the only factors of 25 are 1,5,and 25 (none of which go into 356) we cannot pull out a common factor from the coefficients. Now lets look at the variables. We can see a common theme of p's and q's, so those would part of our GCF. Looking at
There's only one p, and since there are at least one p in each polynomial, then p is part of our GCF.

Now lets look at q. The lowest degree of q is , so thats part of our GCF also.So our full GCF is

Notice that we can divide the GCF cleanly in all of these problems and get
,, and
This is like dividing real numbers by their factors
and
Hope this helps.