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Prime factor question

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Prime factor question

by ramamgr » Thu Apr 10, 2008 4:57 pm
Can someone help me with this question?
For every positive 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) betwwen 30 and 40
e) greater than 40
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Re: Prime factor question

by netigen » Thu Apr 10, 2008 9:02 pm
I think the way to solve this is to find out the prime factors of h(100) which in this case are:

47, 43, 41, 37, ....., 2

How we know 47 is a factor?

47* 2 = 94 and since we know 94 is a factor so 47 is also a factor

Since all primes from 2 to 47 are factors of h(100) they can not be factors of h(100)+1 so the ans will be E

Let me know if this is correct.
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by ramamgr » Fri Apr 11, 2008 8:47 am
Yes, the answer is E. I am not sure whether that's the right approach.
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