Question

Give examples of coprime where the numbers are (i) primes (ii) composite (iii) prime and composite.

Answer 1

Hint: In this question, we have to give examples of coprime. For this, we will first understand the meaning of coprime and then try to find some examples as per our requirement. At last, we will check if the two numbers chosen are coprime or not.

Complete step by step answer:
Here, we need to give examples of coprime where the numbers are (i) prime (ii) composite (iii) prime and composite. Let us first understand the meaning of coprime. Coprime numbers are the numbers which have only 1 as their common factor i.e. their HCF will be 1. Coprime numbers are also known as relatively prime or mutually prime numbers.
Now let us try to find our required examples.
(i) We need to find a pair of coprime numbers which are itself prime numbers. As we know that, every prime number has only 1 its factor, so any two prime numbers are coprime.
Let us take two prime numbers as 3 and 5.
Since both have a common factor as 1 only so (3,5) is our required example.
(ii) We need to find two composite numbers which are coprime. Let us look at the numbers 15 and 16.
Factors of 15 are: 1, 3, 5, 15.
Factors of 16 are: 1, 2, 4, 8, 16.
 Since both of them have only 1 as a common factor, so these are coprime. So (15,16) is our required example.
(iii) We need to find a composite number and a prime number which are coprime. Let us look at the numbers 3 and 4.
Factors of 3 are: 1, 3.
Factors of 4 are: 1, 2, 4.
As we can see 3 has no other factors than 1 and itself. So 3 is a prime number. Also 4 has one other factor that 1 or itself. So it is a composite number. Since both of them have only 1 as a common factor, so these are coprime. So (3,4) is our required example.

Note: Students should note that coprime numbers are also called mutually prime numbers or relatively prime numbers. Students should note that, 1 is coprime with every number. Any two consecutive numbers are always coprime. Any two even integers can never be coprime.