Mathematics is an important subject of many competitive examinations like Bank exams, SSC exams, CDS, NDA, DSSSB exams etc., and its easy to score in Mathematics, so one must prepare well for this section to succeed in various exams.

The preparation of Mathematics begins with study of Number System. Here, we are providing our readers, the basic concepts of Number System and will explain how to solve questions from this unit.

The preparation of Mathematics begins with study of Number System. Here, we are providing our readers, the basic concepts of Number System and will explain how to solve questions from this unit.

**Types of Numbers**

Natural Numbers :Counting numbers (1, 2, 3, 4, 5, 6,........ so on) are called natural numbers. These are also called

Natural Numbers :

*counting numbers*some times. The set of Natural Numbers is denoted by

*in short.*

**N****= {1, 2, 3, 4, 5, ................}**

*N***Whole Numbers :**The natural numbers together with '0' form Whole Numbers. So,

*Whole Numbers*= {0, 1, 2, 3, 4, .............}

Note : Every natural number is a whole number but 0 is a whole number which is not natural number.

**Integers :**All natural numbers, zero (0), and negatives of natural numbers together are called Integers. The set of Integers is denoted by

**in short.**

*Z***= {..........., -3, -2, -1, 0, 1, 2, 3, ...................}**

*Z*

__Few thing to keep in mind:__

Set of positive integers = {1, 2, 3, 4, 5, ............}

Set of negative integers = {-1, -2, -3, -4, ............}

Set of non-positive integers = {0, -1, -2, -3, .........}

Set of non-negative integers = {0, 1, 2, 3, 4, ........}

**Even Numbers :**If a number is divisible by 2, it is called an even number.

**Odd Numbers :**If a number is not divisible by 2, it is called an odd number.

**Prime Numbers :**A number which is not divisible by any number except for 1 and itself, is called an Prime Number.

All Prime Numbers less than 100 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

**Composite Numbers :**The natural numbers which are not prime are called composite numbers.

**Co Prime Numbers :**Two natural numbers

*a*and

*b*are said to be Co Prime numbers if their Highest Common Factor (HCF) is 1.

Example - (2, 3), (4, 5), (7, 9), (12, 17), (18, 19) etc. are pairs of co-primes.

Questions on Number System will be discussed after studying the Divisibility Rules.