##### 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.

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