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

Question

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

prep_gmat · Answer

500 leading zeros.
2005/5+2005/25+2005/125+2005/625

HongHu · Answer

I would guess 420 zeros in the end. If it is close, then I will explain.

MA · Answer

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.

HongHu · Answer

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

Vijo · Answer

All the best Honghu............

ywilfred · Answer

hi, could you explain the reasoning behind this method ?? It seems pretty handy =)

swath20 · Answer

Didnt understand the expalnation, could somebody explain

HongHu · Answer

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.

swath20 · Answer

Thanks Hong Hu that was great

ywilfred · Answer

was the question 2005! meant 2005 factorial ? (i.e. 2005*2004*2003.....*1)

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

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