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# If n is a positive integer greater than 1

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If n is a positive integer greater than 1 [#permalink]  15 Jul 2013, 07:40
If n is a positive integer greater than 1, what is the smallest positive difference between two different factors of n?

Suppose this is a question stem of a DS problem, how would you rephrase this statement ?

a.) Since the smallest positive difference between any two different factors of n is n. Would you rephrase the question as:
If n can be any one of 2,3, 4..., what is the value of n ?

or

b.) Would you go one step ahead and say what is the smallest possible value of n ?
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Re: If n is a positive integer greater than 1 [#permalink]  15 Jul 2013, 08:06
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AbhiJ wrote:
If n is a positive integer greater than 1, what is the smallest positive difference between two different factors of n?

Suppose this is a question stem of a DS problem, how would you rephrase this statement ?

a.) Since the smallest positive difference between any two different factors of n is n. Would you rephrase the question as:
If n can be any one of 2,3, 4..., what is the value of n ?

or

b.) Would you go one step ahead and say what is the smallest possible value of n ?

Your conclusion in (a) is not correct.

Generally the smallest positive difference between two different factors of some integers is greater than or equal to 1. For example:

If n=2, then the smallest positive difference between two different factors of n is 1 --> 2-1=1.
If n=3, then the smallest positive difference between two different factors of n is 2 --> 3-1=2.
If n=4, then the smallest positive difference between two different factors of n is 1 --> 2-1=1.
If n=5, then the smallest positive difference between two different factors of n is 4 --> 5-1=4.
If n=6, then the smallest positive difference between two different factors of n is 1 --> 2-1=1.
If n=7, then the smallest positive difference between two different factors of n is 6 --> 7-1=6.
...
If n=9, then the smallest positive difference between two different factors of n is 2 --> 3-1=2.
...
If n=15, then the smallest positive difference between two different factors of n is 2 --> 3-1=2.
...

Basically if n=even, then the smallest positive difference between two different factors of n is always 1.
If n is odd, then the smallest positive difference between two different factors of n is even, so greater than 1.

Does this make sense?
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Re: If n is a positive integer greater than 1 [#permalink]  15 Jul 2013, 08:44
My bad, mistook factors for multiples.
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Re: If n is a positive integer greater than 1   [#permalink] 15 Jul 2013, 08:44
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