Natural Numbers and Whole Numbers

In Mathematics, the Number system consists of all types of numbers used to perform various calculations. These numbers include natural numbers and whole numbers, prime numbers and composite numbers, integers, real numbers and imaginary numbers etc.

Natural numbers and whole numbers, we have studied since our primary classes. Natural numbers are set of positive integers, whereas natural numbers and zero(0) are called whole numbers, where zero is an undefined identity that produces a null result. Zero is the primary difference between natural and whole numbers.

Natural and whole numbers in Maths have equal importance. Suppose, if we have to count for a number of objects, then we start from numbers 1,2,3,4 and so on, but once these objects are all vanished, what count it gives is zero. There is a further classification of natural numbers. Let us have a look at the brief about both natural numbers and whole numbers in this article.

Natural Numbers

Natural numbers are the set of positive integers, from 1 to ∞ , but it doesn’t include fractional and decimal numbers. They are also known as counting numbers.

Natural Numbers: 1, 2, 3, 4, 5, 6,…….,∞

Types of natural numbers:

• Prime Numbers
• Even and Odd numbers
• Composite numbers
• Co-prime numbers
• Perfect numbers

Learn more about natural numbers here.

Whole Numbers

Whole numbers are also a set of positive integers, including 0, i.e. from 0 to ∞. They also don’t include fractional and decimal parts.

Whole Numbers: 0, 1, 2, 3, 4, 5, 6,…….,∞

To understand more about whole numbers, visit here.

Natural Numbers and Whole Numbers Properties

Both natural numbers and whole numbers follow several properties under addition, subtraction, multiplication and division. They are:

• Closure property
• Commutative property
• Associative property
• Distributive property

However, these properties can be defined based on the operator defined below:

Addition Property

When two natural numbers are added, it results in a natural number only.

Eg: 34 + 45 = 79

When two whole numbers are added, it results in the whole number only.

Eg: 6 + 0 = 6

Subtraction Property

When two natural numbers are subtracted, it may or may not result in a natural number.

Eg: 5 – 2 = 3 is natural number

But 2 – 5 = -3 is not a natural number

The same is the condition for whole numbers. If two whole numbers are subtracted, it is not necessary to result in the whole number.

Multiplication Property

When two natural numbers or whole numbers are multiplied, then it always results in natural numbers and whole numbers, respectively.

Eg: 2 X 6 = 12 is a natural number

4 X 0 = is a whole number, where 4 and 0 are also whole numbers.

Division Property

Division of two natural numbers and whole numbers may or may not result in natural and whole numbers, respectively. If the result is in fraction or decimal, they are not considered natural and whole numbers.

E.g.: 4/2 = 2 is natural, as well as the whole number

But 5/2 = 2.5 is neither a natural nor a whole number.

Additive identity

The number 0 is called the additive identity for both natural and whole numbers. Thus, the addition of any natural number or whole number with 0 gives the number itself.

E.g. 4 + 0 = 4

Here, 4 is a natural number as well as a whole number.

Multiplicative identity

1 is called the multiplicative identity for both natural numbers and whole numbers. Multiplying any natural number and whole number by 1 results in the same natural number or whole number.

E.g. 9 × 1 = 9

0 × 1 = 0

Video Lesson on Numbers

Solved Examples

Example 1: Which of the following is not a natural number?

1. 1
2. 0
3. 7
4. 100

Solution:

Correct option: (b)

Natural numbers: 1, 2, 3, 4,…, 100,…

Whole numbers: 0, 1, 2, 3,…

Thus, 0 is not a natural number.

Example 2: Choose the whole numbers from the following.

9, -3, 0, 28, ½, -1, 14, 9/10

Solution:

Whole numbers include all the positive integers and 0.

So, the whole numbers from the given list are: 9, 0, 28, 14.

To learn more about numbers, download BYJU’S – The Learning App today!