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I remember someone posted a very elegant solution to this problem before.
Here is how:
the number of 0's in the 100! will equal to number of 10 multiples in the 100!
for example, if there are 4 10's
a * b * 10 * d * e * 10 * 10 * f * 10
there wil be 4 0's in the result.
now to find number of 10's we need to:
- find number of 5's in 100! prime factorization
- number of 2's in 100! prime factorization
the min of two will be result.
in this case number of 5's will be alot less that number of 2's so the ans to this question drills down to:
- number of 5's in 100!
which is 100/5 + 100/25
= 24
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