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2005! = x How many zeros does x have? I am sorry if the

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mr_sarn
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2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   11 Feb 2005, 17:29
2005! = x
How many zeros does x have?

I am sorry if the problem is not quite clear.

Whoever knows how to solve this type of problem, please tell me.

Thanx



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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   Updated on: 12 Feb 2005, 01:46
500 leading zeros.
2005/5+2005/25+2005/125+2005/625

Originally posted by prep_gmat on 11 Feb 2005, 21:00.
Last edited by prep_gmat on 12 Feb 2005, 01:46, edited 3 times in total.
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   11 Feb 2005, 22:08
I would guess 420 zeros in the end. If it is close, then I will explain.
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MA
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   11 Feb 2005, 23:07
mr_sarn wrote:
2005! = x, How many zeros does x have?

I am sorry if the problem is not quite clear. Whoever knows how to solve this type of problem, please tell me. Thanx


1-10=2 zeros
11-20=2 zeros
similarly 1-100=(10X2)+1 (1 zero from 100) =21 zeros

101-1000=(21X10)+1 (1 zero from 1,000) = 211 zeros
similarly, 1001-2000= 211 zeros
2001-2005 = 1 zero

altogather = 211+211+1=423.
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   11 Feb 2005, 23:31
My method is the same as prep_gmat's. :)

Though I have miscalculated, it looks like.

It would be something like this
401+80+16+3=500
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   14 Feb 2005, 08:10
All the best Honghu............
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   14 Feb 2005, 08:15
hi, could you explain the reasoning behind this method ?? It seems pretty handy =)
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   14 Feb 2005, 12:38
Didnt understand the expalnation, could somebody explain
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   14 Feb 2005, 12:47
2*5=10 1 zero
4*25=100 2 zeros
8*125=1000 3 zeros
16*625=10000 4 zeros

Since there are plenty of even numbers so you will have sufficient 2's. Therefore to get 0s in the end you need to count how many 5s you have from 1-2005.

Therefore you got 2005/5=401
Here you've counted all the 25s once, but you know each 25 will produce two zeros, so you need to add one more zero for each 25
Therefore you got 2005/25=80
and so on.
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   14 Feb 2005, 16:27
Thanks Hong Hu that was great
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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink] New post   14 Feb 2005, 19:26
was the question 2005! meant 2005 factorial ? (i.e. 2005*2004*2003.....*1)



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Re: 2005! = x How many zeros does x have? I am sorry if the [#permalink]
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