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Factor in a large number

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Factor in a large number

by Anindya Madhudor » Tue Nov 13, 2012 8:07 am
Can anyone please help me show how to solve the following?

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

a) between 2 and 10
b) between 10 and 20
c) between 20 and 30
d) between 30 and 40
e) greater than 40

OA: E
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by eaakbari » Tue Nov 13, 2012 8:56 am
This seems like a toughie,


By taking 2 as common, we can rewrite h(100) as

2^50x(1x2x3x...x50).

Hence every number from 1 to 50 is a factor of 100

So every h(100) + 1 will not be a factor and will leave remainder as one (including primes).

Hence the smallest prime will be above 50.

Answer E seems to fit the description.

Hence E

P.S. Whats the source of the question.
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