how to tackle this question?

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magicalhat: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Jun 04, 2011 7:09 am

by magicalhat » Thu Jun 20, 2013 9:35 pm

What is the greatest integer, n, such that 10^n is a factor of 24! ?

I know it requires prime factorization, but I'm stumped after that....

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Source: Beat The GMAT — Problem Solving | Thu Jun 20, 2013 9:35 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Thu Jun 20, 2013 10:14 pm

First we need to find how many trailing zeroes are in 24!
to find # of trailing zeros = 24 / 5 = 4
so 24! has 4 trailing zeros

4 trailing zeros mean 10^4 therefore n = 4

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aaggar7: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 11, 2012 8:48 pmFollowed by: 1 member; Thanked: 9 times

by aaggar7 » Fri Jun 21, 2013 1:27 am

Every pair of 5 and 2 will make a 10.

So,we need to calculate the number of 5s and 2s in 24!.
It is better to calculate 5s than 2s because 5s will be less than 2s.

So - 5
10
15
20

Hence n = 4.

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