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?
Select the correct option.
A) Between 2 and 20
B) Between 10 and 20
C) Between 20 and 30
D) Between 30 and 40
E) Greater than 40
h(n) = the product of all even integers from 2 to n inclusive   =&gt; h(100) + 1 = (2 * 4 * 6 * 8 * ....... * 100) + 1   = 2^50 * (1*2*3*4*......*50) + 1   As all the numbers from 2 to 50 are factors of 2^50 * (1*2*3.....*50), none of these can be factors of 2^50 *   (1*2*3*4*......*50) + 1 (i.e. of h(100)+1)   Therefore the smallest prime factor of h(100) + 1 is greater than 50.   This corresponds to option (Greater than 40)
<result>E</result>
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?