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Factor of K

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Master | Next Rank: 500 Posts
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by Dean Jones » Sun Dec 25, 2011 11:47 am
Dear Friends,

I was having problems in answering the following question.

Does the integer k have a factor p such that 1<p<k?
1). k>4! 2). 13!+2<= k<=13!+13


Please help.

OA after some discussions.

Regards
Deano.
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by apex231 » Sun Dec 25, 2011 3:06 pm
Does the integer k have a factor p such that 1<p<k?


1). k>4! - not sufficient

2). 13!+2<= k<=13!+13 -> 13! is a multiple of numbers from 1 till 13.

13!+2 - multiple of 2 (because 13! is a multiple of 2)
13!+3 - multiple of 3 (because 13! is a multiple of 3)
.
.
13!+13 - multiple of 13

Hence, if k lies between 13!+2<= k<=13!+13, it will be a multiple of any number from 1 to 13. Hence Stmt 2 is sufficient.
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