Number System - 1

In aptitude we first start with the Number system.

Here, numbers are divided in some category i.e. Natural number, Whole number, Integer, rational number, irrational numbers etc.

Natural numbers:- It is start from 1 to infinity and it is non-negative numbers.
Set of natural numbers is {1, 2, 3, ……}

Whole number:- It is also non-negative number including “0”.
Natural number including “0” is called Whole Numbers.
Set of whole numbers is {0, 1, 2, 3, …….}

Integers:- All numbers are called integer it may be positive or negative.
Set of Integers is {……,-3, -2, -1, 0, 1, 2, 3,……}

Rational number:- Any number that can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero is called Rational number.
Set of rational number is ½, 3/5, -8/5, 0, +3, -150, …….

Irrational number:- Any real numbers are called Irrational number which is not a Rational number.
Set of irrational number is π, √2,√5,√7, …….

Some numbers are like √-8,√-7,√-5,√-1,3+√-7 and so on. These are undefined numbers, called Complex numbers.

Integers- There are three types of integers :-
Positive integers:- 1, 2, 3,………
Negative integers:- -1, -2, -3, ………….
Non-negative integers:- 0, 1, 2, 3, ….

Some other numbers type:-


Even Number:- A counting number which divisible by 2 is called an even number.
Eg.:- 0, 2, 4, 6, 8, ……

Odd number:- A counting number which is not divisible by 2 is called an odd number.
Eg.:- 1, 3, 5, 7, ……….

Prime number:- A number is called a prime number if it has exactly two factors, namely itself and 1.
Eg.:- 2, 3, 5, 7, 11, 13, 17, 19, ……..

Co-primes number:- Two natural numbers a and b are said to be a co-prime if their HCF is 1.
Eg.:- (2, 3), (4, 5), (7, 9), (8, 11)… etc.