Question

What are co-primes? Give examples of five pairs of co-primes. Are co-primes always prime? If no, illustrate your answer by an example.

Answer 1

Hint: In this question, we have to know that in number theory, if the only positive integer separating both of them is 1, the two integers a and b are said to be relatively prime, mutually prime, or co-prime. Therefore, any prime number which divides one does not divide the other. This is equivalent to 1, being their largest common divisor

Complete step by step answer:
First, we have to find out, what are co-primes?
So,
If its elements share no common positive factor except 1., a set of integers can also be called a coprime. Pairwise coprime is a stronger condition on a set of integers, meaning that a and b are coprime for every pair (a, b) of different integers in the set. The set {2,3,4} is coprime but, since 2 and 4 are not relatively prime, it is not pairwise coprime.
Five pairs of co-primes.
Pairs of co-primes means those pairs whose common positive factor is 1.
Pairs are: ( 2, 3 ), ( 3, 4 ), ( 4, 5 ), ( 5, 6 ), ( 6, 7 ) .
Now, we have to state that, are co-primes always prime?
So, its answer is NO. We can illustrate this by taking a pair of 14 and 15 as an example. These are co primes but here we can see that 14 is not a prime number because it is divisible by 7. So, we can say that co-primes are not always prime.

Note:
In such a type of question we have to know what are prime numbers, co-prime numbers and all those terms which are relating the question. Then we will obtain the pairs of co-primes according to the properties of the co-primes and also, we will take some examples so that we can clearly justify our statements.