Problem Solving

Can someone pls explain steps in solving this? Thanks!

For every positive 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 - 10
B) between 10 - 20
C) between 20 - 30
D) between 30 - 40
D) > 40

I am not too sure about this. May be someone can correct me if am wrong.
h(100)=(2*4...100)=2(1*2*3...*50)=2(50*51)/2=2550.

Now prime factors for h(100)=2*17*5*3 which is >40. 1 is neither prime nor composite so i am leaving it. Hence Ans.) D ?

- Deepak

Good explanation here:

https://www.manhattangmat.com/forums/for ... t1152.html

That said, Deepak, I think the formula that you used below (1*2*3*...50)=(50*51)/2 only works for an additive formula, not a product formula.

(1+2+3+4+5) = (5*6)/2 = 15
BUT (1*2*3*4*5) does not = (5*6)/2 = 15, actual is 120.