Problem Solving

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

Can someone solve this?

Thanks.

i would say answer E

h(n)=2^n * n!

h(100)=2^50 * 50!
h(100) is divisible by any numer between 2 and 50, the prime factor being 2

h(100)+1 would leave a reaminder of 1 if divided by numbers ranging from 2 to 50 so I would expect that the smallest prime factor would be at least > or = to 51, so largely over 40, i.e. answer E

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