Two or more numbers that have no common factors other than 1. The numbers themselves may or may not be prime, but they are said to be "prime, relative to each other."
Two numbers are relatively prime when the only factor they share is 1. In other words, their greatest common factor (GCF) is 1.
For example:
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8 and 9 are relatively prime. The factors of 8 are 1, 2, 4, 8. The factors of 9 are 1, 3, 9. The only factor they share is 1, so their GCF is 1.
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6 and 10 are not relatively prime. They share the common factor 2.
An important point: the numbers themselves do not need to be prime. 8 and 9 are both composite numbers, yet they are relatively prime to each other. What matters is not whether each number is prime on its own, but whether they share any common factors.
Relatively prime numbers are also called coprime. This concept is especially useful when simplifying (or reducing) a fraction to its simplest form when the numerator and denominator are relatively prime.
When Do Students Learn About Relatively Prime Numbers?
Students build toward this concept through their work with factors and the greatest common factor.
Grades 4–6 – Factors and Greatest Common Factor
Students find factors of whole numbers and identify the GCF of pairs of numbers, developing the skills needed to recognize when two numbers are relatively prime.
Grades 6–8 – Relatively Prime in Fractions and Ratios
Students apply the concept of relatively prime numbers when simplifying fractions and ratios to their lowest terms.
Grades 9+ – Relatively Prime in Number Theory
Students encounter relatively prime numbers in more advanced contexts, including modular arithmetic, number theory, and algebraic reasoning.
