Help! Prep

For every positive integer n, the fuction 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:

1)   between 2 and 10

2)   between 10 and 20

3)   between 20 and 30

4)   between 30 and 40

5)   greater than 40

Please give some details about how to work it out?

Thanks for answering,

I understand

h(100)=2*4*6*8*...*98*100

=>2^50(1*2*3*...*49*50)

=>h(100)can be divided by any integers between 1 and 50

but why the following?

For example, 18=17+1,

17 can only be divided by 1, 17.

but the smallest prime factor of 18 should be 2?

Is this reasoning wrong? Or ....?

By the way ,  the answer is E for the question.