Greatest possible value of n

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this?

If 10^n is a factor of the product of the first 24 positive integers, what is the
greatest possible value of n?

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

OA: D


Thanks for your help.

Best Regards,
Sri

Good Problem ,

product of the first 24 positive integers

=> 24 *23 *22 *21 .............. 2 * 1 = 24!

10^n is a factor of the product

Remember 10^n means any number which is a multiple of 10

what is the greatest possible value of n?

To find the greatest possible value of " n " we need to find the number of multiple of 10

Or , Practically speaking we need to count to number of zero's in the product of 24!


So work out -

Number of zero's in 24! is nothing but the number of 5's in it , so calculate the total number of 5's in the product of 24!

This is nothing but -

24/5 => 4 leaving remainder 4


So we have 4 fives in 24!

Hence the maximum value of " n " is 4...