Question

What is co-prime ?

Answer 1

Hint: We have to solve this question by stating the definition of co - prime numbers . We will also give examples of some of the co - prime numbers . We will also state how to find whether a set of given numbers are co - prime numbers or not . We will also state the various properties of the co - prime numbers.

Complete step-by-step solution:
A set of given numbers is said to be co - prime numbers if and only if the highest common factor I.e. the H.C.F. of the set of numbers is \[1\] . The co - prime numbers are also known as relatively prime or mutually prime numbers , as they have only \[1\] as their common factors among the set of numbers .
Check for the set of numbers to be co - prime numbers :
Let there be two numbers \[5\] and \[6\] .
Now , we will first write the numbers in terms of its prime factors as :
\[5 = 1 \times 5\]
\[6 = 1 \times 2 \times 3\]
Hence , we can conclude that the highest common factor of the two numbers \[5\] and \[6\] is \[1\] .
Therefore , the numbers \[5\] and \[6\] are co - prime numbers as the highest common factor of the two numbers is \[1\] .

Note: For solving such types of problems we should have the knowledge of properties of coprime numbers. The various properties of co - prime numbers are stated as below :
\[\left( 1 \right)\] Every number is a co - prime with \[1\] .
\[\left( 2 \right)\] Every set of prime numbers are co - prime numbers .
\[\left( 3 \right)\] Any two consecutive numbers or integers all always co - prime numbers .
\[\left( 4 \right)\] The sum of two numbers is always co - prime with the product of the two numbers .
\[\left( 5 \right)\] Two even numbers can never be a set of co - prime numbers as they will always have a common factor \[2\] .