Prove that two consecutive positive integers are always coprime. – InterviewSolution

1.

Prove that two consecutive positive integers are always coprime.

Answer»

Let the numbers be I, I + 1:

They are co-prime if only +ve integer that divides both is 1.

I is given to be +ve 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. Hence the result.

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