Factorial question

Expert replies

jnellaz: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Oct 20, 2008 7:03 pmFollowed by: 5 members; Thanked: 4 times

by jnellaz » Mon Dec 01, 2008 1:14 pm

How many zeros does 1000! end with?

a) 248
b) 249
c) 250
d) 500
e) 625

[spoiler]Answer: B. 249[/spoiler][spoiler]
[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Dec 01, 2008 1:14 pm

muzali: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Fri Sep 28, 2007 10:16 am; Thanked: 6 times; GMAT Score:710

by muzali » Mon Dec 01, 2008 3:01 pm

I found a comprehensive solution here:
https://www.rain.org/~mkummel/stumpers/28jan00a.html

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jnellaz: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Oct 20, 2008 7:03 pmFollowed by: 5 members; Thanked: 4 times

by jnellaz » Tue Dec 02, 2008 6:26 am

Thanks again!

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Tue Dec 02, 2008 6:30 am

5*2=10 (more 2's in 1000! than 5's hence 5 is the limiting factor that detremines the number of 0's)

Shortcut:

Divide 1000 by increasing powers of 5 till u get 0 as the quotient

1000/5+1000/25+1000/125+1000/625+1000/625*5

200+40+8+1+0

= 249

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