Number properties

[viveksunder.vs]

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)greater than 40

How do you find the prime factors for such problems?

[RonPurewal]

this is quite possibly the most frequently posted problem on this whole forum.

here are a couple of resources:
post14808.html
post5477.html

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you don't FIND the prime factors in a problem like this; the whole point of the problem is that there AREN'T any prime factors within a certain range (i.e., 50 or below).

in fact, finding prime factors of large numbers is so hard that it forms the basis for essentially all modern cryptography. so yeah, you don't want to try to find the prime factors in this problem.