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# How many zeros does 100! end with? 20 24 25 30 32 from the

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Director
Joined: 14 Oct 2003
Posts: 588
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, 20:55
How many zeros does 100! end with?

20
24
25
30
32

from the challenge archive.

ty!
Manager
Joined: 19 Nov 2004
Posts: 59
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[#permalink]  10 Dec 2004, 03:12
My answer is B 24
If it is correct, I'll explain why
CIO
Joined: 09 Mar 2003
Posts: 464
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[#permalink]  10 Dec 2004, 12:20
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.
Manager
Joined: 19 Nov 2004
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[#permalink]  10 Dec 2004, 12:38
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
CIO
Joined: 09 Mar 2003
Posts: 464
Followers: 2

Kudos [?]: 33 [0], given: 0

[#permalink]  10 Dec 2004, 12:45
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!
[#permalink] 10 Dec 2004, 12:45
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# How many zeros does 100! end with? 20 24 25 30 32 from the

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