Coprime Numbers: While studying about numbers, students come across with different types of numbers; such as – odd numbers, even numbers, whole numbers, natural numbers, real numbers, integers, prime numbers, composite numbers etc. A prime number is defined as a number which is divisible by 1 and itself only. A prime number does not have any divisors other than one and itself. There is one more type of numbers studied in number theory, these are termed as relatively prime numbers. Two positive numbers are said to be co-prime/relatively prime if they have no common factor other than 1.
In other words, if there are two positive integers which are not evenly divisible by any number except for 1, then both numbers are said to be relatively prime or coprime (co-prime) or mutually prime. We can also say that the greatest common factor of two relatively prime numbers is one. Relatively prime numbers are represented by (a , b) = 1, since the notation (a , b) is used for greatest common factor. Hence if (a , b) = 1, i.e. GCF of a and b is , then a and b would be relatively prime numbers.
For example – 3 and 7 are coprime numbers, since both have no factor in common, other than 1.
In brief, the points to be remembered for coprime numbers are –
- If any two positive integers are coprime means both two numbers do not share any common factors apart from 1.
- The greatest common divisors are denoted by the notation (x, y). Here the relatively prime integers are x and y, that means (x, y) =1.
- Relatively prime integers are commonly known as the Co-prime.
- Two prime numbers are always relatively prime.
Coprime Numbers Definition
Two numbers are said to be coprime (relative prime) if their greatest common factor is one. The integer a = 11 and b = 17 are relative prime because gcd ( 11, 17) = 1
Two integers a, b > 0 are called coprime/relatively prime if they have no common divisor greater than 1.
That is (a, b) = 1
What is coprime Number?
coprime number (Relatively prime) shows that, the greatest common factor between two numbers is always 1. If two numbers are relatively prime, then their greatest common factor is 1. Two integers “a” and “b” are said to be relatively prime if their greatest common divisor is 1. If greatest common factor of two numbers will be greater than one then numbers are not relatively prime.
Steps to Find the Coprime Numbers
Here we discuss some steps for finding the coprime numbers.
Steps to Find the coprime/relatively prime numbers:
Step 1: Factor each number into their prime factors.
Step 2: Match the prime numbers that appear in both factorizations.
Step 3: If greatest common factor is one, then numbers are relatively prime.
Coprime Numbers List
List of coprime numbers between 1 to 100:
- (99,100) and so on.
There are several pairs of co-prime numbers between 1 and 100. The above list are some of coprime numbers to understand the concept.
Coprime Number Examples
Below you can see the examples on relatively prime number –
Question 1: Check whether 10 and 9 is relatively prime
Factors of 10 are 1, 2, 5, 10.
Factors of 9 are 1, 3, 9.
GCD (10 , 9) = 1
So 10 and 9 are relatively prime.
Question 2: Check 6 and 23 relatively prime or not
Given numbers are 6 and 23
factors of 6 are 1, 2, 3, 6.
23 is a prime number.
GCD of (6 , 23) = 1
So 6 and 23 is relatively prime.
Question 3: Check for relatively prime 21 and 14
Given numbers are 21 and 14
factors of 21 is 1, 3, 7, 21
factors of 14 is 1, 2, 7, 14
GCD of (21,14) = 7
So 21 and 14 are not relatively prime.
Question 4: Check whether 7 and 13 is relatively prime
Given numbers are 7 and 13
7 is a prime number
13 is also a prime number
So GCD of (7,13)=1
So 7 and 13 are relatively prime.