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) +2, then p is?	Choose the correct choice from the following answers.
A) between 2 and 20
B) between 10 and 20
C) between 20 and 30
D) between 30 and 40
E) 2
h(100)+2=2∗4∗6∗...∗100+2h(100)+2=2∗4∗6∗...∗100+2 . Notice that we can factor out 2 from h(100)+2, thus the smallest prime factor of h(100)+2 is 2: h(100)+2=2∗(4∗6∗...∗100+1)h(100)+2=2∗(4∗6∗...∗100+1).   Answer: 2.
<result>E</result>
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) +2, then p is?