Okay, I think I understand what you're after.
At the end of this answer is a link to a Gist that solves this problem. I'm not entirely sure it's what you are after, alas... it's my best guess.
The algorithm consists of five steps:
- Build the list of factorial members.
- Calculate and group Prime Factors of factorial members.
- Distribute Prime Factors over powers of 10.
- Multiply Prime Factors, carrying overflow up into the next decimal place.
- Print the solution.
It is inspired by the method described here on math.stackexchange.com. I strongly suggest reading both the question and answer linked before examining the Gist.
Now that that's been said, the Gist can be found here. It is very rough, meant only as a quick demonstration of the method.
I hope it helps you. Best of luck.