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h(n) is the product of the even numbers from 2 to n,

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Manager
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h(n) is the product of the even numbers from 2 to n, [#permalink] New post 14 Oct 2007, 18:17
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h(n) is the product of the even numbers from 2 to n, inclusive, and p is the least prime factor of h(100) +1. What is the range of p?

Please explain.

Thanks a lot
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Re: GPrep - PS ( What is the range of p?) [#permalink] New post 14 Oct 2007, 19:05
humtum0 wrote:
h(n) is the product of the even numbers from 2 to n, inclusive, and p is the least prime factor of h(100) +1. What is the range of p?

Please explain.

Thanks a lot


h(100) = 2^50 * 50!

Let's check the prime numbers. 2 is the factor of h(100), so it can not be the factor of h(100)+1. Same applies to 3,5,7,11,13,17,19,23,29,31,37,41,43 and 47. But we cannot say the same about 53, since 53 is not a factor of h(100). So at least p>47.
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 [#permalink] New post 17 Oct 2007, 17:40
How did you get to 2*4*6...*98*100 = 2^50 * 50 ?
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 [#permalink] New post 17 Oct 2007, 17:47
Big-O wrote:
How did you get to 2*4*6...*98*100 = 2^50 * 50 ?


originally its 2*4*6*8*10*12 etc...

you divide 2 by each of these u get

1*2*3*4*5*6*etc... since you have 50 even integers you get 50 two's or

2^50. then u gotta multiply 2^50*1*2*3*4*5*6....47*48*49*50.

Essentially u are dividing everything by 2 up to 100. U could write every number out but thats a waste of time.

u get 47 as the highest prime. so u know p>47.
  [#permalink] 17 Oct 2007, 17:47
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