Positive even integers and prime numbers

lavinia wrote:For every positive even integer n, the function f(n) is defined to the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of f(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

Answer: [spoiler](E)[/spoiler]

How do you solve this kind of problem?

Thanks!

goyalsau wrote:

lavinia wrote:For every positive even integer n, the function f(n) is defined to the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of f(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

Answer: [spoiler](E)[/spoiler]

How do you solve this kind of problem?

Thanks!

This problem has been discussed many times on this forum ,
I would recommend you to do some search on the forum because posting the problem.

lavinia wrote:Hi Goyalsau,

I've searched this problem, but I couldn't find it. If you have the exactly post, I really appreciate your help.

Thanks!

goyalsau wrote:

lavinia wrote:For every positive even integer n, the function f(n) is defined to the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of f(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

Answer: [spoiler](E)[/spoiler]

How do you solve this kind of problem?

Thanks!

This problem has been discussed many times on this forum ,
I would recommend you to do some search on the forum because posting the problem.

justvishu4 wrote: This problem has been discussed many times on this forum ,
I would recommend you to do some search on the forum because posting the problem.

goyalsau wrote:

justvishu4 wrote: This problem has been discussed many times on this forum ,
I would recommend you to do some search on the forum because posting the problem.