What is co prime numbers explain with examples?

Aug 09, 2022, 16:45 IST

Consider a set of two numbers, if they have no positive integer that can divide both, other than 1, the pair of numbers is co-prime.

Example 1: 21 and 22

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For 21 and 22:

Here 21 and 22 have only one common factor that is 1. Hence, their HCF is 1 and are co-prime.

Example 2: 21 and 27

For 21 and 27:

Here 21 and 27 have two common factors they are 1 and 3. HCF is 3 and they are not co-prime.

Properties of Co-Prime Numbers

Some of the properties of co-prime numbers are as follows.

1 is co-prime with every number.
Every prime number is co-prime to each other: As every prime number have only two factors 1 and the number itself, the only common factor of two prime numbers will be 1. For example, 2 and 3 are two prime numbers. Factors of 2 are 1, 2 and factors of 3 are 1, 3. The only common factor is 1 and hence is co-prime.
Any two successive numbers/ integers are always co-prime: Take any consecutive number such as 2, 3 or 3, 4 or 5, 6 and so on; they have 1 as their HCF.
The sum of any two co-prime numbers are always co-prime with their product: 2 and 3 are co-prime and have 5 as their sum (2+3) and 6 as the product (2×3). Hence, 5 and 6 are co-prime to each other.