Question

Which of the following statements is/are correct?

• A. If two numbers are coprime to each other, then both the numbers must be prime.
• B. Two different prime numbers are always coprime to each other.
• C. Every natural number is coprime with $1.$
• D. Two even numbers can never be coprime to each other.

Answer 1

Answer: (B), (C), (D)

The correct options are
B Two different prime numbers are always coprime to each other.
C Every natural number is coprime with $1.$
D Two even numbers can never be coprime to each other.

If two numbers are coprime to each other, then it is not necessary that they are prime. Eg: $(4,9)$

Two different prime numbers are always coprime to each other as they have only one common factor i.e. $1.$

Every natural number is coprime with $1$ as they have only one common factor i.e. $1.$

Two even numbers can never be coprime to each other as they have atleast two common factors i.e. $1,2.$