Hi, today am going to discuss about **types of numbers** in mathematics. In general we have so many types of numbers are there in maths. In our daily life these types of numbers plays an important role. So let’s see what are the **different types of numbers** and its definitions with some example.

**Types of Numbers:**

**Natural Numbers: **

Counting numbers are called Natural Numbers.

It is denoted by ‘N’.

The set of Natural Numbers are represented by N= {1, 2, 3———}

Smallest number in Natural Number is 1.

Largest Number in Natural Number is can’t be defined.

**Successor:**

For any given Natural Number, add one to that number is called Successor.

Eg: successor of 5 is 5+1=6.

**Predecessor:**

In any given Natural number, subtract one to that number is called predecessor.

Eg: predecessor of 8 is 8-1=7

**Whole Numbers:**

Natural Numbers including zero is called whole numbers. It is denoted by ‘W’.

The set of Whole Numbers are represented by W= {0, 1, 2……..}

Smallest number in Whole Number is 0.

Largest Number in Whole Number is can’t be defined.

- All Natural numbers are Whole numbers but not all whole numbers are Natural numbers.

**Even Numbers: **

The Natural Numbers which are exactly divisible by 2 are called even numbers.

The set of even numbers are denoted by ‘E’.

E= {2, 4, 6, 8…………..}

**Odd Numbers:**

The Natural Numbers which are not exactly divisible by 2, leaves remainder 1 are called as odd numbers.

The set of odd numbers are denoted by ‘O’.

O= {1, 3, 5, 7…………..}

**Properties of Even and Odd numbers:**

- The sum of any two even numbers is an even number.

Eg: 2+4=6

18+20=38

- The difference of any two consecutive even numbers is an even number.

Eg: 20-18=2

14-6=8

- The product of any two even numbers is an even number.

Eg: 24=8

64=24

- The sum of any two odd numbers is an even number.

Eg: 3+3=6

20+20=40

- The difference of any two consecutive odd numbers is an even number.i.e, 2

Eg: 9-7=2

19-17=2

- The product of any two odd numbers is an odd number.

Eg: 57=35

117=77

- The sum of one even and one odd number is always an odd number.

Eg: 11+12=23

- The product of one even number and one odd number is an even number.

Eg: 34=12

- General form of an odd number = 2n-1
- General form of an even number=2n

**Types of numbers based on number of factors:**

**Prime Numbers:**

A prime number has only two factors one and itself. It is greater than ‘1’.

Eg: 2, 3, 5, 7…………

**Composite Numbers:**

A Natural number having at least three factors.

- 1 is neither prime nor prime

Eg: 4 is a composite number?

Factors of 4= 1, 2, 4

Yes 4 is a composite number it has three factors.

**Multiple:**

The product of a number and counting numbers are known as multiples of that number.

Eg: multiples of 4 are 4, 8, 12, 16………….

- Every multiple of a number is greater than or equal to that number.
- The number of multiples of a given number is infinite.

**Factor:**

If a number ‘x’ divides another ‘y’ exactly then that x is a factor of y.

- Every factor of that number is less than or equal to that number.
- Number of factors of a given number is finite.

Eg: 6 divide 18 exactly

Then 6 is a factor of 18.

**Prime factor:**

If a factor of a given number is prime, then the factor is called a prime factor.

Eg: factors of 30 are 1, 2,3,5,6,10,15,30.

Out of these prime factors are 2, 3, and 5

**Twin Primes:**

The difference of pair of prime numbers is 2.

Eg: (11, 13), (17, 19)

**Perfect number: **

A number in which sum of all its factors is equal to twice the number is called a perfect number.

Eg: 28 is a perfect number or not?

Factors of 28 =1, 2,4,7,14,28

Sum of factors = 1=2+4+7+14+28=56 =2(28)

So, 28 is perfect number.

**Amicable numbers:**

Two numbers are said to be amicable numbers, if the sum of the divisors of one number excluding itself is equal to the other number.

Eg: 220 and 284 are amicable numbers

Sum of divisors of 220 (except 220) = 1+2+4+5+10+11+20+22+44+55+110=284

Sum of the divisors of 284(except 284) = 1+2+4+5+71+142=220

**Relatively prime numbers:**

Two positive integers ‘a’ and’b’ are said to be relatively prime or co- primes, If they do not have any common factor other than one.

Eg: 25 and 81 are co-primes.

I hope you liked the post on **types of numbers**. In future I will update the **classification of numbers** according to its nature and its importance.