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

n should be 2 since factors of 2007 are 223 and 9 so after  cancelling 2007 we can only cancel its factors

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.