Which term describes a number that shares only the number 1 as a common factor with another number?

The term that describes a number sharing only the number 1 as a common factor with another number is known as co-prime. When two integers are co-prime (or relatively prime), their greatest common divisor (GCD) is 1, meaning there are no other common factors between them aside from 1. For example, the numbers 9 and 28 are co-prime because the only positive integer that divides both is 1.

Understanding co-primality is crucial in the realm of encryption and number theory, particularly in algorithms like RSA, where the selection of co-prime numbers for keys is necessary for ensuring the security of the encryption process. Co-prime numbers are integral in creating a pair of keys that can operate together without sharing factors that could compromise their security.

The other terms, such as prime numbers, refer specifically to numbers that have exactly two distinct positive divisors: 1 and the number itself. Composite numbers are defined as numbers that have more than two positive divisors, meaning they can be divided evenly by more than just 1 and themselves. Integers encompass all whole numbers, both positive and negative, as well as zero, and do not pertain specifically to the concept of sharing factors.