CAT Definition and examples of Prime, Composite and Co-prime numbers - Practice Questions & MCQ

List of Prime, Composite and Co-prime Numbers - Definition and Examples

Definition of Prime Numbers: 

Prime numbers are positive integers greater than 1 which have no divisors other than 1 and itself. In other words, prime numbers have exactly two factors.

Example: 2, 3, 5, 7, 11, 13, 17, 19, 23 etc.

Definition of Composite Numbers: Composite numbers are positive integers greater than 1 which have more than two factors. In other words, composite numbers can be divided by at least one number other than 1 and itself.

Example: 4, 6, 8, 9, 10, 12, 14, 15, 16 etc.

Definition of Co-prime Numbers: Co-prime numbers are a set of numbers whose greatest common divisor (GCD) is 1. In simple terms, there is no common factor, other than 1, between two co-prime numbers.

Example: (2, 5), (7, 9), (13, 16), (21, 25) etc.

Tips and Tricks:

• To determine whether a number is prime or not, divide it by prime numbers less than its square root. If no prime number divides the given number, then it is a prime number.
• Two numbers are co-prime if their GCD is 1.
• The factors of composite numbers always include the number itself and 1.
• When two numbers are co-prime, their product is also coprime with both of them.

Solved Example:

Question: Find the number of composite numbers between 1 and 50.

Solution: Prime numbers between 1 and 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Total prime numbers = 15. Hence, total composite numbers = 50 - 15 = 35.

Question: Which of the following pairs are co-prime numbers? 

(i) (21, 31) 

(ii) (12, 25) 

(iii) (8, 9) 

(iv) (20, 23)

Solution: (i) GCD(21, 31) = 1. Hence, (21, 31) are co-prime.

(ii) GCD(12, 25) = 1. Hence, (12, 25) are co-prime.

(iii) GCD(8, 9) = 1. Hence, (8, 9) are co-prime.

(iv) GCD(20, 23) = 1. Hence, (20, 23) are co-prime.

Therefore, pairs (i), (ii), (iii), and (iv) are all co-prime numbers.

Question: Which of the following numbers are prime? 

(i) 51 (ii) 37 (iii) 39 (iv) 43

Solution: (i) 51 is divisible by 3, hence not a prime number.

(ii) 37 has exactly two factors, 1 and 37. Hence, it is a prime number.

(iii) 39 is divisible by 3, hence not a prime number.

(iv) 43 has exactly two factors, 1 and 43. Hence, it is a prime number.

Therefore, numbers (ii) and (iv) are prime numbers.

Remember to practise more questions based on prime, composite, and co-prime numbers to gain a better understanding of these concepts and their applications in various problem-solving scenarios.