1977 AHSME Problems/Problem 25
Determine the largest positive integer such that is divisible by .
We first observe that since there will be more 2s than 5s in , we are looking for the largest such that divides . We will use the fact that:
(This is an application of Legendre's formula).
From and onwards, . Thus, our calculation becomes
Since none of the answer choices equal 250, the answer is .