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compute the largest positive integer n such that (2007)!/(2007)^n is an integer.

compute the largest positive integer n such that (2007)!/(2007)^n is an integer.
 

Grade:11

2 Answers

anonymus
18 Points
6 years ago
n should be 2 since factors of 2007 are 223 and 9 so after  cancelling 2007 we can only cancel its factors
anonymous
16 Points
6 years ago
the factors of 2007 are 223 and 3. Since no. of 3s in 2007! is much more than the no. of 223s in it ; we can get the answer by calculating no. numbers in 2007! which are divisible by 223, which we can get by using [2007/223]+[2007/223^2]+........
this way the answer is 9.

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