##### Number System for Aptitude

There are lot's of categories in Number system we will be talked about it, but the first question arise here is-

**What is Number?**

**Ans**. A *number* is a mathematical object used to count, measure, and label.

**What is System?**

**Ans**. A *system* is a collection of elements or components that are organized for a common purpose.

So, if we Combined both of them then what we get ??

** "A set of values used to represent different quantities is known as ***Number System***".**

**Different types of Numbers?**

1. Natural Numbers

2. Whole Numbers

3. Integers

4. Rational Numbers

5. Irrational Numbers

6. Even Number

7. Odd Number

8. Composite Number

9. Prime Numbers

10. Co-Prime Numbers

11. Twin-Prime Numbers

Let's talk about every number in detail one by one.

**Note -: '0' is not a natural number.**

**Natural number: -**Counting numbers are called natural numbers.

Example:- 1, 2, 3,4,5,6------ are all natural numbers.maximum natural

number ∞**Whole numbers: -**All counting numbers together with zero from the set of whole numbers

Example:- 0, 1, 2, 3, 4, ------ are whole number.**Integers: -**All counting numbers, 0 and -ve of counting numbers are called integers.

Example:- -∞---------, -3, -2, -1, 0, 1, 2, 3, -------∞**Rational Numbers: -**A Rational Number is a real number that can be written as a simple fraction

Example:- {p/q/p,q∈Z}**Irrational Numbers: -**An Irrational Number is a real number that cannot be written as a

simple fraction.

Example:- √2,√3......**Even numbers: -**A number divisible by 2 is called an even number.

Example:- 0, 2, 4, 6, - - - - - - - - -**Odd numbers: -**A number not divisible by 2 is called an odd number.

Example:- 1, 3, 5, 7, - - - - - -**Composite Numbers: -**Numbers greater than 1 which are not prime, are called composite numbers.

Example:- 4, 6, 8, 9, 10, - - - -. 6 -> 1,2,3,6.**Prime Numbers: -**A number greater than 1 having exactly two factors, namely 1 and itself is called

a prime number.

**Upto 100 prime numbers are:**

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97**Co-prime Numbers: -**Two natural numbers a and b are said to be coprime if their HCF is 1.

Example:- (21, 44), (4, 9), (2, 3), - - - - -**Twin prime numbers: -**A pair of prime numbers (as 3 and 5 or 11 and 13) differing by two are

called twin prime number.

Example:- The twin pair primes between 1 and 100 are

**(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).**

So finally, that's the sweet story of Number System, Hope you like it.