What are the Various Types of Numbers in maths?

Types of Numbers

Hello Aspirants!

In this post, we will deal with various types of numbers in the number system.

Under this section " Number System: Various Types of Numbers " we will deal with the following :
  • Natural Numbers
  • Whole Numbers
  • Integers
  • Prime Numbers
  • Composite Numbers
  • Even Numbers
  • Odd Numbers
  • Rational Numbers
  • Irrational Numbers
  • Real Numbers
Let's Start the Tutorial!

Natural Numbers: All numbers which are used for counting is called Natural Number. As the counting starts from 1, so all numbers including 1 and above are called a natural number. For example : 1, 2, 3, 4, 5, .......

Note: Natural Numbers are also known as Counting Numbers.

Natural Numbers are represented as " N " where N = { 1, 2, 3, 4, 5, ....  }

Smallest Natural Number is 1 and Largest Natural Number is 

0 ( zero ) is not a natural number

Whole Numbers: All natural numbers including 0 ( zero ) is known as the whole number. As the whole number starts from 0 ( zero ), so all numbers including 0 ( zero ) and above are called a whole number. For example : 0, 1, 2, 3, 4, .......

Whole Numbers are represented by " W " where W = { 0, 1, 2, 3, 4, 5, .....  }

Smallest Whole Number is 0 and the Largest Whole Number is 

Integers: All natural numbers and their negatives and 0 ( zero ) is called integers. For example : -2, -1, 0, 1, 2, .....

Integers are represented by " Z " where Z = { -, ..... -3, -2, -1, 0, 1, 2, 3, .....  }

The largest integer is  and the Smallest integer is -

Prime Numbers: Positive Whole Numbers which are greater than 1 and have only two factors namely 1 and the number itself are called prime numbers. For example : 2, 3, 5, 7, 11, ......

Composite Numbers: Positive Whole Numbers which are greater than 1 and have more than two factors are called Composite Numbers. For example : 4, 6, 8, 9, 10, ......


Even Numbers: All integers which are exactly divisible by 2 i.e. if the required integers are divided by 2, it yields 0 ( zero ) as the remainder, then the required integers are called even numbers. For example : ..... -4, -2, 2, 4, ......


Odd Numbers: All integers which are not exactly divisible by 2 i.e. if the required integers are divided by 2, it yields a non-zero number as the remainder, then the required integers are called odd numbers. For example : .... -5, -3, 3, 5, .....


Rational Numbers: A number in the form of fraction p/q where q is not equal to zero is called a rational number. For example 2/5, 1/2, 1/3...


Every integer is a rational number. For example, -2 can be expressed as -2/1 and thus it is a rational number

Irrational Numbers: A number that cannot be written in the form of a fraction P/q where q is not equal to zero is called an irrational number. For example  √2, √3 .....


All non-terminating, non-repeating decimals are irrational numbers.

The square root of any prime number is an irrational number


Real Numbers: A number which is either from a set of rational numbers or from irrational numbers are called real numbers. 

In other words, Real Numbers are numbers that can be represented in decimal that have a finite or infinite sequence of digits to the right of the decimal point. A real number can be positive, negative, or zero.


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