Lyndon explains why this is one of his favourite NRICH problems.
I like the twist that means you need to take a little care - you need to worry about detail.
Although it uses factorial notation, this is only a very minor part of the problem- basically it means you can make your point succinctly - that is what mathematical notation is all about.
My additional question of how many zeros also points out that an apparently closed problem can be easily opened up, with further questions to be asked.
This problem is a special case of Factorial Fun.
See also Powerful Factorial
and Factoring Factorials
which are also special cases.