2006 AIME A Problems/Problem 3
Problem
Let be the product of the first positive odd integers. Find the largest integer such that is divisible by
Solution
Note that the product of the first positive odd integers can be written as
Hence, we seek the number of threes in decreased by the number of threes in
There are
threes in and
threes in
Therefore, we have a total of threes.
For more information, see also prime factorizations of a factorial.