Hello, VENI!

Amazing . . . you did it all wrong and got the right answer!

It has nothing to do with the powers-of-2.How many 0's are at the end of 100! ?

Question: how many factors-of-5 are in 100-factorial?

Reasoning: Each factor-of-5, paired with any even number, will produce a zero at the end.

Since half the numbers are even, there are plenty of even numbers available.

So how many factors-of-5 are there?

Well, everyfifthnumber is a multiple of 5.

. . So there are: . of them.

But some of them are multiples of , which provide an extra factor of 5.

. . And there are: . of them.

Hence, there are: . factors-of-5 in 100-factorial.

Therefore, it ends in 24 zeros.