What is the primary feature of co-prime numbers?

Co-prime numbers, also known as relatively prime numbers, are defined by the characteristic that their greatest common divisor (GCD) is 1. This means that the only positive integer that can evenly divide both numbers is 1. The concept of co-primality is vital in number theory and has implications in various areas, such as cryptography and modular arithmetic.

Co-prime pairs can be, for example, (14, 15) or (8, 9). In both instances, the GCD is 1, making them co-prime. This property is significant because it influences the behavior of numbers in mathematical operations, particularly in algorithms related to encryption and data security.

The other characteristics presented in the question—being both odd, both even, or both composite—do not define co-prime numbers, as co-primality does not depend on the parity (odd or even) or the composite nature of the numbers. Thus, the defining feature that accurately describes co-prime numbers is that their greatest common divisor is 1.