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
SOL:   Lets consider h(100):   =&gt; 2*4*6*8.........*98*100   =&gt; (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50)   =&gt; (2^50) * (1*2*3*4........*49*50)   =&gt; h(100) = (2^50) * (50!)   We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100).   But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50;   ANSWgreater than 40R: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?