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The smallest whole number is zero, as the set of whole numbers starts from zero and increases by 1 along the positive direction of the number line.
Are all natural numbers whole numbers?
Yes, all natural numbers are whole numbers because the set of natural numbers is 1, 2, 3, 4 … and so on.
Are all integers whole numbers?
No, not all integers are whole numbers. Integers include all positive and negative natural numbers, whereas whole numbers only include zero and positive numbers.
What is the value if a whole number is divided by zero?
The division of a whole number by zero is undefined.
What are Whole Numbers? Definition and Examples
Whole numbers include zero and all positive integers. Learn the important properties of whole numbers with solved examples here.
Nikita Aggarwal13 Aug, 2025
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Whole numbers form the foundation of basic mathematical calculations. From counting objects to measuring quantities and distance, whole numbers are useful in everyday life.
It is a collection of all the numbers starting from zero and going to infinity. No fractions or decimals; these are just simple positive numbers. This article discusses the important properties of whole numbers in detail.
The definition of whole numbers states that it is a set of all positive, countable numbers, along with the number zero. Fractions, decimals, or negative numbers are not whole numbers. Therefore, we can say that whole numbers consist of 0, 1, 2, 3, 4, 5… and so on.
For example, 8, 33, 276, and 1045 are all whole numbers.
Numbers like 22/7, 1.73, -14, 0.54, etc. are not whole numbers.
The set of whole numbers is represented by the symbol W. Therefore, we can write W = {0, 1, 2, 3, 4, 5, 6 …}
Whole Numbers on a Number Line
According to the whole number definition and examples, we can easily represent them on a number line that starts from zero and increases by 1 at an equal distance from left to right along the line.
The arrow indicates that whole numbers continue to infinity.
As per the definition of whole numbers, they include all positive numbers plus zero. Natural numbers are also all positive numbers, but they don’t include zero. In other words, natural numbers are a subset of whole numbers.
Let’s look at the primary differences between whole numbers and natural numbers as mentioned in the table below.
Whole Numbers
Natural Numbers
Whole numbers are 0, 1, 2, 3, 4, 5 …
Natural numbers are 1, 2, 3, 4, 5, …
The minimum whole number is 0
The minimum natural number is 1
All whole numbers except zero are natural numbers
All natural numbers are whole numbers
Properties of Whole Numbers
After getting an idea of what whole numbers are, it is necessary to understand the properties of whole numbers, which help in performing mathematical calculations conveniently and accurately. The four main properties of whole numbers are as follows:
Closure Property
Commutative Property
Associative Property
Distributive Property
We will explain these properties in detail with the whole numbers and examples.
Closure Property of Whole Numbers
According to this property, when we add or multiply two whole numbers, we always get a whole number as the sum or product, respectively. We can never get a negative, fraction, or decimal number by adding or multiplying two whole numbers.
For example, let’s take two whole numbers, 7 and 12.
By adding, we get 7 + 12 = 19. Here, 19 is a whole number.
Again, by multiplying we get 7 x 12 =84. Here, 84 is a whole number.
According to this property, when two whole numbers are added or multiplied, the addition or multiplication can be done in any order, and the sum or product will always be the same.
If a and b are two whole numbers, a + b = b + a and a x b = b x a.
For example, for two whole numbers, 15 and 23, we get:
15 +23 = 38 and 23 + 15 =38
The sum is the same in both cases, although the order changes.
Similarly, for two whole numbers, 10 and 18, we get
10 x 18 = 180 and 18 x 10 =180
The product is identical in both cases, even if the order changes.
Associative Property of Whole Numbers
According to this property, in case of addition or multiplication of three whole numbers, they can be grouped in any order, and the result will be the same.
It means, if p, q, and r are three whole numbers, then we can say, p + (q + r) = (p + q) = r
For example, let’s add three whole numbers: 6, 7, and 8.
Option 1: 6 + (7 + 8) = 6 + 15 = 21
Option 2: (6 + 7) + 8 = 13 + 8 =21
So, regardless of the grouping, the sum remains the same.
Again, for example, multiply three whole numbers: 2, 3, and 4.
Option 1: (2 x 3) x 4 = 6 x 4 = 24
Option 2: 2 x (3 x 4) = 2 x 12 = 24
So, no matter how the numbers are arranged, the product will always be the same.
Distributive Property of Whole Numbers
This property of whole numbers states that the multiplication of a whole number is distributed over the sum of the other two whole numbers.
It means that if x, y, and z are three whole numbers, then the sum of y and z multiplied by x gives the same result when y and z are multiplied by the same number x and then added.
In other words, x (y + z) = x.y + x.z
Let’s take an example.
There are three whole numbers: 3, 5, and 9.
Now, we calculate 3 x (5 + 9) = 3 x 14 = 42
Again, 3 x 5 + 3 x 9 = 15 +27 = 42
Therefore, we can say: 3 x (5 + 9) = 3 x 5 + 3 x 9
