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, every fifth number 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.