Co – Prime Numbers

What are Co-prime Numbers?

The pairs of numbers that do not have any common factor other than one are co-prime numbers.

Let a and b are two positive integers are called co-prime numbers, if the only one 1 as their common factor. (a, b) is said to be a co-prime pair.

Definition: Two numbers which do not have any common factor other than 1, and greatest common factor (GCF) of these numbers is 1, are called “Co-Prime Numbers”.

or simply, 

Two numbers having only 1 as a common factor are called “Co – Prime Numbers.”

How to find Co-prime Numbers?

To find any two numbers are co-prime, first we find their Greatest Common Factor (GCF).

If their GCF is 1, then the numbers are co-prime.

Example: Let us consider two numbers 9 and 10.

The factors of 9 is 1, 3 and 9.

The factors of 10 is 1, 2, 5, and 10.

The common factors of 9 and 10 is 1.

GCF of (9, 10) is 1.

Thus, (9, 10) is co-prime numbers.

Example: 12 and 15

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 15 are 1, 3, 5, and 15.

Here, 12 and 15 have two common factors, they are 1 and 3.

GCF of 12 and 15 is 3, so they are not co-prime numbers.

Example: 4 and 25

Common factors of 4 and 25

The factors of 4 are, 1, 2 and 4.

The factors of 25 are, 1, 5 and 25.

The number 1 is the factor of both 4 and 25.

So, these two numbers have only 1 as the common factor.

Thus, 4 and 25 are co-prime numbers.

similarly 7 and 15,

12 and 49,

21 and 22,

5, 7 and 9 etc. are co-prime numbers.