GCD problem

[just4myself]

What is the greatest common factor of the positive integers j & k?
1. k=j+1
2. jk is divisible by 5

OA = A

Please give your explanations...

Thank you...

[pepeprepa]

You can try a little if like me you don't find it obvious:
20 and 21
1 and 2
15 and 14
19 and 18
1 and 0

It seems that 2 consecutive positive integers have 1 as greatest factor. Try to take several examples to be sure there is not an exception.

[Ian Stewart]

Yes, the GCD of two consecutive positive integers is always 1. Say x and x+1 are consecutive positive integers, and say d is a divisor of x. That is, x is a multiple of d. Then the nearest multiples of d to x are x+d and x-d; x+1 can't be divisible by d if d > 1. So if d is a divisor of x, d is never a divisor of x+1, unless d is equal to 1.