Number System - Types of Number

This post forms a basis of many other topics in quantitative aptitude . Let us

begin by understanding various types of numbers.

(1) Natural Numbers: All the counting numbers are called natural

number.

Example: 1, 2, 3, 4, 5, ......

(a) Even Numbers: The numbers which are exactly divisible by 2 are

called even numbers.

Example: 2, 4, 6, 8, ...

(b) Odd Numbers: The numbers which leave a remainder 1 when

divided by 2 are called odd numbers.

Example: 1, 3, 5, 7, ....

(c) Prime Numbers: If a number is not divisible by any other number

except 1 and itself, it is called a prime number.

Example: 2, 3, 5, 7, 11, ....

Co-primes ® Two numbers which have no common factor

between them except 1 are said to be co-prime to each other. The

two numbers individually may be prime or composite.

Example: 13 and 29 are co-primes.

(d) Composite Numbers: Numbers which are divisible by other

numbers along with 1 and itself are called composite numbers.

Example: 4, 6, 8, 9, 10, .....

The number 1 is neither prime nor composite.

(2) Whole Numbers: Natural numbers along with ‘0’ form the set of

whole numbers.

Example: 0, 1, 2, 3, .....

(3) Integers: All counting numbers and their negatives along with zero

are called Integers.

Example: ......-4, -3, -2, -1, 0, 1, 2, 3, 4, .......

(4) Rational and Irrational Numbers: Any number which can be

expressed in the form of p

q , where p and q are integers and q¹ 0, is a

rational number.

Example:

3

5 , 4, –6, etc.

Numbers which are represented by non–terminating and non–

recurring decimals are called irrational numbers.

Example: 2 = 1.414....., 3 = 1.732.....

(5) Real Numbers: Rational and irrational number taken together are

called real numbers