Let be the maximum such that

First note that so the number of 0s at the end of will be exactly

For example for we have , note that the coefficients of the multiples of 5 are the maximum powers of 5 dividing these numbers. This comes from - (k,5)=1- So the maximum power of 5 dividing the number is itself multiplied by the maximum such that

Now since it follows that the maximum such that is

Thus:

It may also be written as: ( note that appears in as many sums as the maximum such that )

PS- That's not a factorial