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Prime factors

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by metalhead » Sat Apr 03, 2010 1:35 pm
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
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Source: — Problem Solving |

by kevincanspain » Sat Apr 03, 2010 2:54 pm
h(100) + 1 = 2x4x6x...x98x100 + 1= (2^50)50! + 1

Since 50! is a multiple of every integer from 2 to 50, h(100) + 1 is 1 greater than a multiple of every integer from 2 to 50, and is thus not a multiple of any integer from 2 to 50. Thus its greatest prime factor is greater than 50
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by metalhead » Sat Apr 03, 2010 5:42 pm
Aah - that makes so much sense now! :) Thanks so much!
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by Shawshank » Sun Apr 04, 2010 2:42 am
metalhead wrote:Aah - that makes so much sense now! :) Thanks so much!
Am still confused,,,

h(100) + 1 = 2(50!) + 1

What after tht ????
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by Stuart@KaplanGMAT » Sun Apr 04, 2010 8:35 am
There are over 50! posts on this question - do a search on h(n) or h(100) to find them.

Here's one:

https://www.beatthegmat.com/gmat-prep-nu ... 8649.html?
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Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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