Problem Solving

For every positive even integer n, the function h(n) is defined to be the product of all 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) between greater than 40

Folk, this problem has been answered sacred number of times on this forum. Please do search the forum before you post your query. Anyway, here is the link where you can find a perfect solution to this question.

https://www.beatthegmat.com/integer-need ... 30927.html

the answer should be C IMO

I really don't know the shortcut but would love to know if someone is aware about

what I did is took product of even numbers from 2 to 10 i.e f(10) add 1
the number comes 3841 which is divisible by 23 a prime number
I believe even if you keep multiplying numbers through 100 for f(100) if added 1, that number will be divisible by 23

others comment please