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factors

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by niraj_a » Sun Dec 07, 2008 9:48 am
If 10^n is a factor of the product of the first 24 integers, what is the greatest possible value of n?

A) 7
B) 6
C) 5
D) 4
E) 3

OA D

i guesstimated 5 = n because 24*20*10*5*2 acount for 4 zeros anyway.
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Re: factors

by Stuart@KaplanGMAT » Sun Dec 07, 2008 9:59 am
niraj_a wrote:If 10^n is a factor of the product of the first 24 integers, what is the greatest possible value of n?

A) 7
B) 6
C) 5
D) 4
E) 3


i guesstimated 5 = n because 24*20*10*5*2 acount for 4 zeros anyway.
For every factor of 10, we need a 2 and a 5.

2 won't be the limiting factor (since every even number has at least 1 factor of 2), so let's focus on the 5s.

Looking at the relevant numbers in 24!:

5*10*15*20

means that we'll have 4 5s on our list. Therefore, the maximum number of 10s we can get is also going to be 4.
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