It is impossible for fac to be non-prime and divide lst the way this algorithm is designed. Even though 4 may be a factor of lst, by the time fac = 4 is the case, lst will already have had all the 2s divided out of it, so lst wont be divisible by 4. The algorithm will short-circuit and iterate on fac.

Is there an answer better than n^2? All the answers I see poster use two FOR blocks.

I think you weren't supposed to sort the array