Question

What do you mean by co–prime numbers? Explain with examples.

Answer 1

Hint: For solving this question you should know about the co–prime numbers. In this problem we will define and explain to co–prime numbers and see the examples of these to understand this clearly.

Complete step by step solution:
According to the question it is asked to explain co – prime numbers and also asked for examples of co – prime numbers.
As we know that co – prime numbers are a set of numbers where the common factor among them is 1. It implies that the HCF or the highest common factor should be 1 for those numbers. Co – prime numbers are also referred to as ‘Relatively Prime Numbers’.
Eg: - If x and y are the co – prime numbers set then the only common factor between these two numbers is 1.
Co – prime numbers from 1 to 100:
Co – prime numbers are none other than just two numbers which have 1 as the common factor. Some of these co – prime numbers from 1 to 100 are –
(1, 99) (29, 31)
(14, 15) (23, 1)
(28, 57) (59, 97) etc.
Co – prime numbers are sets of numbers which do not have any common factor between them other than one. This means that their highest common factor is one.
Eg. Check that the given sets are co – prime numbers or not.
(i) 14 and 15
(ii) 15 and 18
Sol: - (i) 14 and 15
Factors of 14 are 1, 2, 7 and 14
Factors of 15 are 1, 3, 5 and 15
So, the common factor between them is 1. So, these are prime numbers.
(ii) 15 and 18
Factors of 15 are 1, 3, 5 and 15
Factors of 18 are 1, 2, 3, 6, 9 and 18
So, the common factor between them is 1 and 3.
So, these are not co – prime numbers.

Note: Some of the properties of co – prime numbers are:
1 is co – prime with every number.
Every prime number is co – prime to each other.
Any two successive numbers are always co – prime.
The sum of any two co – prime numbers are always coprime with their product.