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 20
B. Between 10 and 20
C. Between 20 and 30
D. Between 30 and 40
E. Greater than 40

Answer: E

Source: GMAT Prep