Properties of Natural Numbers
All the natural numbers have these properties in common :
- Closure property
- Commutative property
- Associative property
- Distributive property
Let’s learn about these properties in the table below.
| Property | Description | Example |
|---|---|---|
| Closure Property | ||
| Addition Closure | Sum of any two natural numbers is a natural number. | 3 + 2 = 5, 9 + 8 = 17 |
| Multiplication Closure | Product of any two natural numbers is a natural number. | 2 × 4 = 8, 7 × 8 = 56 |
| Associative Property | ||
| Associative Property of Addition | Grouping of numbers does not change the sum. | 1 + (3 + 5) = 9, (1 + 3) + 5 = 9 |
| Associative Property of Multiplication | Grouping of numbers does not change the product. | 2 × (2 × 1) = 4, (2 × 2) × 1 = 4 |
| Commutative Property | ||
| Commutative Property of Addition | Order of numbers does not change the sum. | 4 + 5 = 9, 5 + 4 = 9 |
| Commutative Property of Multiplication | Order of numbers does not change the product. | 3 × 2 = 6, 2 × 3 = 6 |
| Distributive Property | ||
| Multiplication over Addition | Distributing multiplication over addition. | a(b + c) = ab + ac |
| Multiplication over Subtraction | Distributing multiplication over subtraction. | a(b – c) = ab – ac |
Note:
- Subtraction and Division may not result in a natural number.
- Associative Property does not hold true for subtraction and division.
Natural Numbers | Definition, Examples & Properties
Natural Numbers are all positive integers from 1 to infinity and are a component of the number system. Natural numbers are also called counting numbers because they are used to count things. Natural numbers do not include 0 or negative numbers.
In this article, we will learn more about natural numbers, their properties, natural numbers from 1 to 100, their types, and examples in detail.
Illustration of Natural Numbers
Table of Content
- What are Natural Numbers?
- Natural Numbers Definition
- Types of Natural Numbers
- Natural Numbers from 1 to 100
- Natural Numbers and Whole Numbers
- Difference Between Natural Numbers and Whole Numbers
- Natural Numbers on Number Line
- Properties of Natural Numbers
- Operations With Natural Numbers
- Sum of First n Natural Numbers
- Examples of Natural Numbers
- Practice Questions on Natural Numbers