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Question
Prove that two consecutive positive integers are always co-prime
Solution
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.
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