PS

[cris]

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 ?

OA: [spoiler]>40[/spoiler]

[gabriel]

According the given information h(100)= 2*4*6*8*10......*100

If we take 2 as common from each of those even number we get h(100)= 2^50 (1*2*3*4*.....*50).

Now, Consider any number, eg. 30 = 1*2*3*5 the prime factors over here are 2,3,5. But if we add 1 to 30 the new number (in this case 31) will not be divisible by any of 30's prime factor i.e. 2,3,5 because though 30 is divisible by 2,3,5 .. 1 is not divisible by either of the three prime factors 2,3,5.

For h(100) the prime factors are all the prime numbers between 1 and 50. Now, when we add 1 to h(100) the resulting number will not be divisible by any of the prime factors of h(100) (the same reason as in the above example)and the smallest prime factor will have to be greater than 49.

[cris]

Thanks a lot gabriel...but why it has to be >49 and not >50?

Update
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Yhinking abiut it it doesnt really matter bc neither 49 nor 50 are primes right? :D

thnaks again gabriel!