Types of number

There are various types of number as follow

1. Natural Number

Nature number are counting number and these are denoted by   ,

  i.e.,             

* All natural number are positive.

* Zero is not a natural number, therefore 1 is the smallest natural number.

2. Whole number

All natural number and zero form the set of whole number and these are denoted by W,

 i.e,                

* Zero is the smallest whole number

* Whole number are also called as non-negative integers.

3. Integers

Whole number and negative number form the set of integers and there are denoted by ,

i.e.,         

Integers are of following two types

1. Positive integers:- Natural numbers are called as positive integers and these are denoted by  ,

i.e.,        

2. Negative integers:- Negative of natural number are called as negative integers and these are denoted by  

i.e.,             

* 0 is neither +ve nor -ve integers.

4. Even number

A counting number which is divisible by 2, is called an even number

For example, 2,4,6,8,10,12,....etc.

* The unit's place of every even number will be 0,2,4,6, or 8.

5. Odd number

A counting number which is not divisible by 2, is called an odd number

For example, 1,3,5,7,9,11,13,15,17,....etc.

* The unit's place of every odd number will be 1,3,5,7 or 9.

6. Prime number

A counting number is called a prime number when it is exactly divisible by only 1 and itself.

For example 2,3,5,7,11,13,.... etc.

* 2 is the only even number which is prime.

* A prime number is always greater then 1.

* 1 is not a prime number therefore the lowest odd prime number is 3.

* Every prime number greater than 3 can be represented by 6n+1, where n is integer.

7. Composite number

Composite number are non-prime natural number. They must have atleast one factor apart from 1 and itself.

For example 4,6,8,9,..etc.

* composite number can be both odd and even.

* 1 is neither a prime number nor a composite number.

8. Coprime

Two natural number are said to be  coprime, if their common divisor is 1

For example (7,9), (15,16), etc.

* coprime number may or may not be prime.

* Every pair of consecutive number is coprime.

9. Rational number

A number that can be expressed in the form of p/q is called a rational number, where p,q are integers and  .

For example   

10. Irrational number

The number that cannot be expressed i  form of p/q are called irrational number, where p,q are integers and .

For example   

*   is an irrational number as 22/7 is not the actual value of   but it is its nearest value.

* Non-periodic infinite decimal fractions are called irrational numbers.

11. Real numbers

Real number  include both rational and irrational number. They are denoted by .

For example