# 100! - 99!

question: what is 100! - 99!

I've broken it down to a problem like this: Let x=99! Then 100! = 100*99! = 100x. 100x - x=99x = 99*99!.

I can't figure out a way to simplify the problem any more than that.

Thank you in advance for any help.

## Answers and Replies

HallsofIvy
Homework Helper
There is the obvious: 100!- 99!= 99!(100- 1)= 99!(99).

phinds
Gold Member
2019 Award
you've got the right answer and I don't see how it COULD be simplified any further except by actually computing 99! which just seems like a waste of time.

1 person
arildno