Last updated on July 5th, 2025
Relative prime numbers are two numbers that have no common factors other than 1. Relative primes are used to identify patterns or simplify fractions. In this article, we will learn how to find relative prime numbers, their properties, and their applications.
Relative prime numbers are also known as co-prime or mutually prime numbers. If a and b are two numbers and their common factor is 1, then they are considered relatively prime. In this instance, the pair (a, b) is called a relatively prime pair. These numbers do not necessarily need to be prime; two composite numbers can also be relatively prime. For example, 9 and 10 are relatively prime, as the common factor is 1.
Here are some interesting fun facts about relatively prime numbers:
Understanding the mathematical properties of relatively prime numbers helps us solve equations and simplify fractions. Here are a few properties to look at:
Now let’s learn how to find the relative prime numbers. To check if two numbers are relatively prime or not, we first find the Greatest Common Factor (GCF) of the given numbers:
Example 1: Determine if 13 and 20 are Relatively Prime
As the GCF(13, 20) = 1. Therefore, the pair (13, 20) is relatively prime.
Example 2: Check if 18 and 24 are Relatively Prime
Since the GCF(18, 24) = 6, the pair (18, 24) is not relatively prime.
In real life, co-prime numbers or relatively prime numbers are used in various fields of computer science, cryptography and many more. Few applications are as following -
Relatively prime numbers are a fundamental concept in math. However, students often make mistakes when finding or identifying them. Here are a few common mistakes and ways to avoid them:
Determine if 9 and 24 are relatively prime.
9 and 24 are not relatively prime.
We first find the factors of each number
Factors of 9: 1, 3, 9
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Now, identify the common factors.
Common factors: 1 and 3
Since 9 and 24 have a common factor greater than 1, i.e., 3, we can confirm that they are not relatively prime.
Determine if 17 and 31 are relatively prime.
17 and 31 are relatively prime.
The first step is to find the factors of the given numbers:
Factors of 17: 1, 17 (since 17 is prime)
Factors of 31: 1, 31 (since 31 is prime)
Then, identify the common factors.
Common factor: Only 1
Now, find the GCF
GCF(17, 31) = 1
Since the GCF is 1, we confirm that 17 and 31 are relatively prime.
Check if 11 and 14 are relatively prime.
the GCF is 1, so we confirm that 11 and 14 are relatively prime.
We first find the factors of the given numbers:
Factors of 11: 1, 11 (since 11 is prime)
Factors of 14: 1, 2, 7, 14
Then, identify the common factors.
Common factor: Only 1
GCF(11, 14) = 1
Here, the GCF is 1, so we confirm that 11 and 14 are relatively prime.
Check if 10 and 21 are relatively prime.
the GCF is 1, so we confirm that 10 and 21 are relatively prime.
The first step is to find the factors of the given numbers separately:
Factors of 10: 1, 2, 5, 10
Factors of 21: 1, 3, 7, 21
Then, identify the common factors.
The only common factor is 1
Now, we find the GCF:
GCF(10, 21) = 1
Here, the GCF is 1, so we confirm that 10 and 21 are relatively prime.
Determine if 12 and 18 are relatively prime.
GCF(12, 18) = 6
The first step is to list the factors separately to find the GCF:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Now, list the Common factors of 12 and 18: 1, 2, 3, 6
Identify the largest common factor among them:
GCF(12, 18) = 6
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.