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Director
Joined: 14 Oct 2003
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Location: On Vacation at My Crawford, Texas Ranch
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How many zeros does 100! end with? 20 24 25 30 32 from the [#permalink]
 09 Dec 2004, 21:55
How many zeros does 100! end with?
20
24
25
30
32
from the challenge archive.
pls explain answer
ty!
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Manager
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My answer is B 24
If it is correct, I'll explain why 
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CIO
Joined: 09 Mar 2003
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I think it's 20.
every zero is going to come from another multiple of 10 in the mix. So 100,90,80,70,60,50,40,30,20,10 each contribute one zero to the total. We now have 10 zeros.
But ten comes from 2x5, so for every 5 that's in this thing, if there's an even to multiply it by, then there's another 10. so 95, 85, 75, 65, 55, 45, 35, 25, 15, 5 all contribute a 5, and there are definately enough even numbers to multiply them all by, so that's another 10 zeros.
Since there's no other way to get zeros, there are 20 contributers, and 20 zeros all together.
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Manager
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1) 100,90,80,70,60,50,40,30,20,10 ELEVEN ZEROS from here
2) 25,50,75 THREE MORE ZEROS
because 25=5x5
50=10x5
75=5x5x5
So 24 total I think 
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CIO
Joined: 09 Mar 2003
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lovely_baby wrote: 1) 100,90,80,70,60,50,40,30,20,10 ELEVEN ZEROS from here 2) 25,50,75 THREE MORE ZEROS because 25=5x5 50=10x5 75=5x5x5 So 24 total I think definately. i missed all those. good catch!
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