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
