**Natural numbers** room a component of the number device which has all the positive integers indigenous 1 till infinity and also are also used for counting purpose. It does not incorporate zero (0). In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers.

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Natural numbers are part of actual numbers, that include only the hopeful integers i.e. 1, 2, 3, 4,5,6, ………. Excluding zero, fractions, decimals and an adverse numbers.

* Note:* herbal numbers carry out not include an unfavorable numbers or zero.

In this article, you will certainly learn an ext about natural numbers through respect to their definition, compare with totality numbers, representation in the number line, properties, etc.

## Natural Number Definition

As explained in the advent part, organic numbers space the numbers which are positive integers and includes number from 1 it rotates infinity(∞). This numbers are countable and are generally used because that calculation purpose. The collection of organic numbers is represented by the letter “**N**”.

**N** = 1,2,3,4,5,6,7,8,9,10…….

## Natural Numbers and Whole Numbers

Natural numbers encompass all the whole numbers excluding the number 0. In other words, all natural numbers are totality numbers, but all entirety numbers space not natural numbers.

Natural number = 1,2,3,4,5,6,7,8,9,…..Whole number = 0,1,2,3,4,5,7,8,9,….Check out the difference in between natural and also whole number to know much more about the distinguishing properties the these two sets of numbers.

The over representation of sets reflects two regions. A ∩ B i.e. Intersection of herbal numbers and also whole numbers (1, 2, 3, 4, 5, 6, ……..) and also the green an ar showing A-B, i.e. Part of the whole number (0).

Thus, a whole number is **“a component of Integers consist of of every the natural number consisting of 0.”**

### Is ‘0’ a organic Number?

The answer come this concern is ‘No’. Together we understand already, natural numbers start with 1 to infinity and also are optimistic integers. Yet when we integrate 0 through a confident integer such together 10, 20, etc. It becomes a organic number. In fact, 0 is a entirety number which has actually a null value.

**Every natural Number is a whole Number. True or False?**

Every herbal number is a entirety number. The statement is true due to the fact that natural numbers room the confident integers that begin from 1 and also goes till infinity whereas entirety numbers additionally include all the optimistic integers in addition to 0.

## Representing natural Numbers top top a Number Line

Natural numbers depiction on a number line is together follows:

The above number heat represents herbal numbers and also whole numbers. All the integers top top the right-hand next of 0 stand for the herbal numbers, thus creating an infinite set of numbers. As soon as 0 is included, this numbers end up being whole numbers which are likewise an infinite collection of numbers.

### Set of herbal Numbers

In a collection notation, the price of natural number is “N” and also it is represented as offered below.

**Statement: **

N = collection of all numbers starting from 1.

**In Roster Form:**

N = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ………………………………

**In collection Builder Form:**

N = x : x is an integer beginning from 1

**Natural numbers Examples**

The organic numbers incorporate the optimistic integers (also well-known as non-negative integers) and also a few examples incorporate 1, 2, 3, 4, 5, 6, …∞. In other words, organic numbers room a collection of every the entirety numbers not included 0.

23, 56, 78, 999, 100202, etc. Are all instances of organic numbers.

## Properties of herbal Numbers

Natural numbers properties space segregated into four main properties which include:

**Closure home**

**Commutative property**

**Associative property**

**Distributive property**

Each of these properties is explained below in detail.

### Closure Property

**Natural numbers are constantly closed under addition and multiplication. **The enhancement and multiplication of two or much more natural numbers will always yield a herbal number. In the case of **subtraction and also division, organic numbers do not obey closure property,** which method subtracting or separating two organic numbers might not offer a herbal number together a result.

**Addition:**1 + 2 = 3, 3 + 4 = 7, etc. In every of this cases, the result number is always a organic number.

**Multiplication:**2 × 3 = 6, 5 × 4 = 20, etc. In this case also, the result is always a natural number.

**Subtraction:**9 – 5 = 4, 3 – 5 = -2, etc. In this case, the result may or might not it is in a organic number.

**Division:**10 ÷ 5 = 2, 10 ÷ 3 = 3.33, etc. In this case, also, the result number may or may not be a herbal number.

Note: Closure building does no hold, if any of the number in situation of multiplication and also division, is not a organic number. However for enhancement and subtraction, if the an outcome is a hopeful number, then just closure residential or commercial property exists.

**For example: **

### Associative Property

The **associative building holds true in instance of enhancement and multiplication of natural numbers **i.e. A + ( b + c ) = ( a + b ) + c and also a × ( b × c ) = ( a × b ) × c. Top top the various other hand, for **subtraction and department of organic numbers, the associative residential or commercial property does not organize true**. An example of this is offered below.

**Addition:**a + ( b + c ) = ( a + b ) + c => 3 + (15 + 1 ) = 19 and (3 + 15 ) + 1 = 19.

**Multiplication:**a × ( b × c ) = ( a × b ) × c => 3 × (15 × 1 ) = 45 and also ( 3 × 15 ) × 1 = 45.

**Subtraction:**a – ( b – c ) ≠ ( a – b ) – c => 2 – (15 – 1 ) = – 12 and ( 2 – 15 ) – 1 = – 14.

**Division:**a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c => 2 ÷( 3 ÷ 6 ) = 4 and ( 2 ÷ 3 ) ÷ 6 = 0.11.

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### Commutative Property

For commutative property

Addition and also multiplication of natural numbers display the commutative property. Because that example, x + y = y + x and a × b = b × aSubtraction and department of natural numbers carry out not present the commutative property. Because that example, x – y ≠ y – x and x ÷ y ≠ y ÷ x### Distributive Property

Multiplication of herbal numbers is constantly distributive end addition. For example, a × (b + c) = ab + acMultiplication of organic numbers is additionally distributive end subtraction. Because that example, a × (b – c) = ab – ac**Read an ext Here:**

### Operations With natural Numbers

An summary of algebraic procedure with organic numbers i.e. Addition, subtraction, multiplication and division, along with their corresponding properties room summarized in the table provided below.