# Natural Numbers : concept, example & properties

## What are Natural Numbers?

Natural numbers are positive integers starting from 1 to infinity.

Features of Natural Numbers
(a) Positive numbers greater than 0
(b) Starts with number 1

What are not natural numbers
(a) 0 & Negative numbers
(b) Decimals and Fraction

### Natural Number Definition

Natural numbers are counting numbers which are part of the set N.

Where, N = { 1, 2, 3, 4, 5 . . . . . infinity}

They are also called counting numbers are they are used in daily activity of counting objects and figures

### Example of Natural Numbers

Any integer number starting from 1 to the highest possible number come under the definition of Natural number

Examples include 1, 9, 25, 100, 9999, 987654, 7895968 etc…

### Set of Natural Number

Given below are set of natural expressed in different forms:

(a) N = Set of positive integer starting from 1

(b) N = {1, 2, 3, 4, 5, 6 . . . . . .}

(c) N = {x : x is an integer starting from 1}

### Why Natural numbers are called Counting number?

In our daily activity, we do some or other kind of counting.

Right from counting number of fruits in the refrigerator to number of currency in the purse, we take the help of natural numbers.

Let me give you one example:

One day your mother asked you to purchase 3 packets of biscuit from the local shop.

You went to the shop & asked for 3 biscuits.

The shopkeeper gave the items & ask for 6 dollars.

You count the money and gave it to the vendor before moving back home

In the whole process, you took the help of natural numbers for counting.

## Difference between Natural number & Whole number

There is just one difference between natural number & whole number.

Whole number includes number 0 in its collection.

Hence, Natural number is a part of whole number except number 0.

The set of natural number and whole number is given as:
Natural Number (N) = { 1, 2, 3, 4, 5, 6, 7 . . . . . }
Whole Number (W) = {0 , 1, 2, 3, 4, 5, 6 . . . .}

## Types of Natural Number

There are basically two types of natural number

### Even Natural Number

All Natural number which are divisible by 2 is known as Even Natural Number

Example of even natural number
2, 16, 98, 980, 9990, 67868 etc..

Note that all the numbers are positive and even.

Even Natural Number expressed in set form
E = { 2x ; where x is any positive integer > 0}

### Odd Natural Number

The natural numbers which are not divisible by 2 is called Odd Natural Number.

Example
3, 15, 99, 873, 7891, 10261

Odd Natural Numbers expressed in set form
O = { 2x – 1, x is any positive integer greater than 0}

## Properties of Natural Number

There are four important properties
(a) Closure Property
(b) Associative Property
(c) Commutative Property
(d) Distributive property

Let us understand each property one by one

(a) Closure Property

It says that the addition and multiplication of natural numbers result in a natural number

Example
(i) 5 + 13 = 18
Addition of natural number 5 & 13 results in 18 which is also a natural number

(ii) 8 x 6 = 48
Multiplication of natural number 8 & 6 results in another natural number 48

(b) Associative Property

It says that addition or multiplication of natural numbers gives same result even after regrouping the numbers

Example

(i) 2 + (3 + 4) & (2 + 3) + 4

⟹ 2 + 7 & 5 + 4
⟹ 9 & 9

Hence, both addition yielded same result

(ii) 5 x (3 x 4) & (5 x 3) x 4

⟹ 5 x 12 & 15 x 4
⟹ 60 & 60

Thus, both multiplication gave same result

(c) Commutative Property

The sum or multiplication of natural number yield same result even if you interchange the digits

Examples

(i) 5 + 6 & 6 + 5

⟹ 11 & 11

Hence, even after interchanging digits, the addition result is same

(ii) 7 x 3 and 3 x 7

⟹ 21 & 21

Hence, even after changing digits the multiplication gave same results

(d) Distributive Property

Given below are distributive property of multiplication

Example
(i) 5 x (4 + 3) & (5 x 4) + (5 x 3 )

⟹ 5 x 7 & 20 + 15

⟹ 35 & 35

Hence, both the expression yield same result

## Frequently asked Questions on Natural numbers

### Is number 0 a part of natural number?

No!!
0 is not a part of natural number.

Natural number starts from 1 and then includes all the positive integer till infinity

### What is the smallest natural number?

Number 1 is the smallest natural number

### Can a negative number like -2 be a natural number?

No!!
Negative numbers are not part of natural number.

Just understand the meaning of word “Natural”
Natural number are easily be found and used in our daily life.

Negative numbers are not natural

### Why all natural numbers are integer?

Integer is a collection of both positive and negative number including 0.

The positive numbers are both integer and natural number

### What are the first ten natural number?

First Ten natural numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10

### Can you represent natural number in number line?

Yes!!
Observe the below number line image