问一道GMATPrep里的数论题，请ＮＮ们帮忙

在做ＧＭＡＴＰrep里的模拟卷时碰到这道数论题，不知道该从何下手，请路过的ＮＮ们帮忙指点迷津，先谢谢了！

For every positive even integer n, the function h(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

A. between 2 and 10

B. between 10 and 20

C. between 20 and 30

D. between 30 and 40

E. greater than 40

正确答案是E