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cool_jonny009
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How many zeros contained in 100!? (a) 100 (b) 24 (c) 97 (d) 12 Nov 2005, 01:18
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How many zeros contained in 100!?

(a) 100
(b) 24
(c) 97
(d) 45
(e) 67



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How many zeros contained in 100!? (a) 100 (b) 24 (c) 97 (d) 12 Nov 2005, 02:35
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there will be 11 zeros for 10, 20, 30, 40, 50, 60, 70,80, 90 and 100

plus there will be 10 zeros for 5, 15............95

for 75 , 25 and 50 there will be 3 additional 0's

so sum it up 11+10+3 = 24

SO b IS MY ANSWER CHOICE
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How many zeros contained in 100!? (a) 100 (b) 24 (c) 97 (d) 12 Nov 2005, 11:57
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cool_johnny,

Istead of an exhaustive method, it there a quick way to solve this question. BTW, I like all the questions you have posted. Where did you get them?
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How many zeros contained in 100!? (a) 100 (b) 24 (c) 97 (d) 13 Nov 2005, 00:08
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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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