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If A, B are two natural numbers >1 and their H.C.F is 1, then which of these statements is always TRUE?
Question

If A, B are two natural numbers >1 and their H.C.F is 1, then which of these statements is always TRUE?

A.

A, B are even consecutive numbers

B.

A, B are coprime to each other

C.

Product AB is a prime number

D.

A, B are both prime numbers

Correct option is B

Explanation:
If the H.C.F. of two natural numbers A and B is 1, it means that the only common factor between A and B is 1. This defines that A and B are coprime to each other.
Thus, the statement A, B are coprime to each other is always TRUE when their H.C.F. is 1.
Option A: A and B are even consecutive numbers. This is not always true, as consecutive numbers can be odd or even.
Option C: Product AB is a prime number. This is not necessarily true. The product of two coprime numbers does not guarantee a prime number.
Option D: A and B are both prime numbers. This is not always true as well. Coprime numbers need not be prime themselves.
Therefore, the correct answer is Option B: A, B are coprime to each other.

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