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Greatest Common Factor

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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Jun 28, 2012 9:29 pm
alex.gellatly wrote:What is the greatest common factor of the positive integers j and k?

1) k = j+1
2) jk is divisible by 5
Statement 1: j and k are consecutive positive integers.
Hence, only common factor of j and k is 1.

Sufficient

Statement 2: Consider the following cases,
j = 1, k = 5 --> GCF = 1
j = 5, k = 5 --> GCF = 5

Not sufficient

The correct answer is A.
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by tutorphd » Fri Jun 29, 2012 5:24 am
The important thing to understand here is why consecutive numbers j and j+1 do not have any other common factors except -1 and 1.

Let's take a factor of j, call it n, and try to divide j+1 by it:

(j+1)/n = j/n + 1/n

j/n is integer since n is a factor of j BUT 1/n is never integer EXCEPT when n = +/- 1. The result j/n + 1/n will be integer only for n = +/- 1 which means j+1 is divisible by a factor of j only when that factor is n = +/- 1.

Similar logic can be applied to the integers j and j+2. The only common factors they will have are +/- 1 and +/- 2.
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by alex.gellatly » Wed Jul 11, 2012 12:46 am
tutorphd wrote:The important thing to understand here is why consecutive numbers j and j+1 do not have any other common factors except -1 and 1.

Let's take a factor of j, call it n, and try to divide j+1 by it:

(j+1)/n = j/n + 1/n

j/n is integer since n is a factor of j BUT 1/n is never integer EXCEPT when n = +/- 1. The result j/n + 1/n will be integer only for n = +/- 1 which means j+1 is divisible by a factor of j only when that factor is n = +/- 1.

Similar logic can be applied to the integers j and j+2. The only common factors they will have are +/- 1 and +/- 2.
Thanks. You made it clear. Can this logic also be applied to the integers j and j+3 and j and j+n (when n is a prime)?
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