Problem Solving

For every positive even integer n, the function f(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40

I guessed greater and 40 since the product will be a large number and it's turns out to be correct, but why?

All I can think of is that the final# ends in 01

Helen I posted this question yesterday (you can find it under the name of "PS") and gabriel gave a fantastic answer...check that post!