Question

Prove that two consecutive positive integers are always co-prime

Answer 1

Let the numbers be I, I + 1

They are co-prime if the only positive integer that divides both is 1.

I is given to be positive integer.

So I = 1, 2, 3, ….

∴ One is odd and the other one is even.

Hence H.C.F. of the two consecutive numbers is 1.