Natural number can be defined as a set of whole numbers that can be used for counting. Natural numbers is the set of positive number. Natural numbers can be divided into different groups according to different properties. When we consider the factor of a number, the set of natural number can be divided into two sets, prime numbers, composite numbers. Natural numbers greater than 1 that are not prime are called composite.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number

What are Prime Numbers in Maths

Any number, that has exactly two factors, that is one and the number itself is called a prime number. The set of prime numbers can also be called odd prime number if 2 is excluded. The only reason is that, the only even prime number is 2. If we remove 2, the remaining numbers becomes the set of all odd prime numbers.
Prime numbers are those numbers that cannot be divided by any number except themselves and one. A Prime Number can be divided evenly only by 1 or itself

Solved Examples

Question 1: Is 2 is a prime number?
Solution:
Factors of 2 are 1 and 2.

=> Yes, 2 is prime number.
 

Question 2: Is 32, is a prime number?

Solution:
Given number = 32

Factors of 32 = 1, 2, 4, 8 and 32

=> A Prime Number can be divided evenly only by 1 or itself.

=> 32 is not a prime number.
 

What are Composite Numbers in Maths

Any natural number that is not prime called a composite number, that is, any number that has factors, other than 1 and the number itself is a composite number. Composite numbers has more than two factors.

Composite number: A natural number greater than 1 that is not a prime number is called a composite number.

Solved Examples

Question 1: Is 6 is a composite number?
Solution:
Number = 6

=> Factors of 6 = 1, 2, 3 and 6.

=> 6 have more than two factors

=> 6 is a composite number.
 

Question 2: Is 35 is a composite number?
Solution:
Number = 35

Factor of 35 = 1, 5, 7 and 35

=> 35 have more than two factors.

=> 35 is a composite number.
 

What are Prime Numbers and Composite Numbers

Natural numbers greater than one that are not prime are called composite numbers. There is only one number, which is neither prime nor composite, that is 1. A Composite Number can be divided evenly by numbers other than 1 or itself. All even numbers are divisible by two and so all even numbers greater than two are composite numbers.
Natural numbers are classified as prime numbers, composite numbers and number neither prime nor composite:
In the set of numbers from 1 to 20,
  • 1 is neither prime nor composite.
  • 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers.
  • 4, 6, 8, 9, 10, 12, 14, 16, 18, and 20 are composite numbers.

1 is neither prime nor composite:

For 1, the factors are 1 and the number 1 itself.

=> Factor of 1 = 1.

But according to the definition of prime, a number can only have 1 and it self as a factors.

=> 1 is not a prime number.     .........................(1)

According to the definition of composite number, a number can have more factors other than 1 and the number itself.

=> For 1, the factors are 1 and the number 1 itself.

=> Factor of 1 = 1.

=> 1 is not a composite number.    .........................(2)

From (1) and (2), we conclude that 1 is neither prime nor composite

One is the only natural number which is neither prime nor composite.

Solved Examples

Question 1: Is 27 a prime number or composite number?
Solution:
Number = 27

Factors of 27 = 1, 3, 9 and 27

=> Factors of 27 are more than two.

=> 27 is a composite number.

 

Question 2: Is 43 a prime number or composite number?
Solution:
Number = 43

Factors of 43 = 1 and 43

=> Factors of 43 are 1 and number itself, so according to the definition of prime number, 43 is a prime number.

=> 43 is a prime number.