Number System - Study Material

 Number System For Bank Exams – Notes, Tips – Tricks And Questions

A number system is defined as a systematic way of expressing numbers. The number system is a mathematical notation for representing numbers of a given set by using a set of digits or symbols in a logical manner. Number System helps to understand the basics of quantitative ability.

The value of any specific digit in a number can be determined by

  • The actual digit
  • Its position in the number
  • The base of the number system

Classification of Numbers:

The number system is classified into following types:

Natural Numbers:

Numbers which are used for counting objects are known as Natural numbers. The natural numbers are denoted by N.

N = {1, 2, 3, 4…………}

Whole Numbers:

Whole numbers are the set of numbers in which zero is included in addition to natural numbers. The whole numbers are denoted by W.

W = {0, 1, 2, 3, 4…….}


Integers include all natural numbers in addition to zero & negative numbers. Integers are denoted by I or Z.

I = {-3, -2, -1, 0, 1, 2, 3…..}

Rational Numbers:

Rational numbers are expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.

Q = 5/6, 7/8 etc.

Irrational Numbers:

The numbers which cannot be expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.

Example - π = 3.141592653589793238….

Prime Numbers:

A prime number is a natural number which is divisible only by 1 and itself. It is greater than 0.

Example - 2, 3, 5, 7, 11, 31, etc.

Composite Numbers:

All the numbers (except 1) which do not fall under the category of prime numbers are known as composite numbers.

Example - 4, 8, 10, 22, 100 etc.

Co-Prime Numbers:

Co-Prime Numbers are the set of integers which have only 1 as their common factor or the highest common factor (HCF) is 1.

Example – 13 & 14 are co-prime.

Even Numbers:

The numbers which are divisible by 2 are known as even numbers.

Example – 2, 4, 6, 8, 10….

Odd Numbers:

The numbers which are not divisible by 2 are known as odd numbers.

Example – 3, 5, 7, 9……

Tricks to remember while solving number system questions:

  • 1 is neither divisible nor prime.
  • Two consecutive odd prime numbers are known as prime pair.
  • All natural numbers are whole, integer, rational and real.
  • All whole numbers are rational, Integer and real.
  • All rational numbers incorporates integers, since every integer can be written as a fraction with denominator 1. Example (9/1).
  • The square of an even is even and the square of an odd number is odd.
  • Any given Prime Number can never be a Composite Number.
  • Fractions are rational.
  • Zero is neither negative nor positive number.
  • If x is any number then, if x divides zero, result will be zero. If 0 divides x, then result will be infinite or not defined or undetermined i.e. 0/x =0, but x/0 =∞ (infinite) where x is real number.
  • The sum and the product of two rational number is always a rational numbers.
  • The product or the sum of a rational number and irrational number is always an irrational number.

Number System Practice Set


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