Difference Between Natural Numbers and Whole Numbers
The concept of natural numbers plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding what natural numbers are helps students master counting, number properties, and solve day-to-day problems quickly and accurately. This page breaks down the definition, properties, solved examples, and common questions about what are natural numbers for easy learning and fast revision.
What Is a Natural Number?
Natural numbers are positive integers that start from 1 and go on without end. In simple words, any number you use for counting objects—like 1, 2, 3, 4, 5, etc.—is a natural number. These are sometimes called counting numbers. The set of natural numbers is usually shown by the symbol N, so N = {1, 2, 3, 4, ...}. In everyday situations such as counting books, measuring time, or numbering days, you are using natural numbers.
Natural Numbers on the Number Line
You can easily spot natural numbers on a number line. They start from 1 and continue rightwards: 1 → 2 → 3 → 4 → 5 → ... Each step on the number line is a natural number. Numbers like 0, negative numbers, fractions, or decimals do not count as natural numbers because you cannot use them for counting whole objects.
Properties of Natural Numbers
| Property | Meaning & Example |
|---|---|
| Closure | Addition and multiplication of any two natural numbers will always give another natural number. Example: 2 + 3 = 5, 2 × 4 = 8 |
| Commutative | Changing the order in addition or multiplication does not change the answer. Example: 3 + 5 = 5 + 3, 2 × 7 = 7 × 2 |
| Associative | Grouping of numbers does not affect sum or product. Example: (1 + 2) + 3 = 1 + (2 + 3) |
| Distributive | Multiplication distributes over addition. Example: 2 × (3 + 4) = 2 × 3 + 2 × 4 |
| Identity | There is no natural number (except 0, which is not natural here) that can be added to a natural number to leave it unchanged; likewise for multiplication, 1 is the identity. Example: 5 × 1 = 5 |
Difference Between Natural and Whole Numbers
| Natural Numbers | Whole Numbers |
|---|---|
| Start from 1 | Start from 0 |
| N = {1, 2, 3, ...} | W = {0, 1, 2, 3, ...} |
| Do NOT include 0 | Include 0 |
Students often confuse zero as a natural number, but it is included only in whole numbers, not in natural numbers.
Examples and Non-Examples of Natural Numbers
| Natural Numbers (✓) | Not Natural Numbers (✗) |
|---|---|
| 1, 2, 3, 4, 7, 15, 28, 100, 205, 1820 | 0, -3, 2.5, 9/2, -1, 1/2, -7 |
Use Cases of Natural Numbers
Natural numbers appear everywhere in daily life and maths:
- Counting objects (e.g., 12 apples)
- Ranking positions (e.g., 1st, 2nd, 3rd place)
- Scoring in games
- Numbering chapters or exercises
- Marking days on a calendar
Solved Examples: Natural Numbers
- Write the first ten natural numbers.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 - Is 0 a natural number?
No, 0 is not included in natural numbers. - Identify the natural numbers among: -2, 7, 0, 3.5, 1
7 and 1 are natural numbers. - List all natural numbers between 10 and 15.
11, 12, 13, 14, 15 - Is 23 a natural number?
Yes, 23 is a natural number because it’s a positive integer used for counting.
Try These Yourself
- Write the first five natural numbers.
- Check if 48 is a natural number.
- Find all natural numbers between 30 and 60.
- Identify non-natural numbers from the list: 12, 15, 18, 0.5, -7.
Frequent Errors and Misunderstandings
- Mistaking 0 or negative numbers as natural numbers
- Thinking decimals or fractions can be natural numbers (like 2.5 or 9/2)
Relation to Other Number Sets
Mastering natural numbers helps in understanding whole numbers, integers, and even more advanced topics like real numbers and prime numbers. Many properties, such as closure or commutativity, are best understood by first learning about natural numbers. Practice with solved examples and quizzes boosts your clarity for any class or exam.
Classroom Tip
An easy trick to remember: natural numbers are the numbers we naturally use to count things, and they always start from 1. Vedantu teachers often use number lines and real-life examples in live classes to help students remember this quickly and avoid confusion in exams.
We explored natural numbers—definition, key properties, solved examples, and tips to avoid mistakes. To get even more confident, try Vedantu’s free live sessions or check out their full set of solved NCERT solutions for Class 6 Maths Chapter 1 and factors and multiples explained.
FAQs on What Are Natural Numbers: Meaning, Symbol & List
1. What are natural numbers in Maths?
Natural numbers are the positive integers used for counting and ordering. They are also known as counting numbers. The set of natural numbers is represented by the symbol N and includes all whole, non-negative numbers starting from 1 and extending to infinity. For example, N = {1, 2, 3, 4, 5, ...}. Numbers like 34, 86, and 10034 are all examples of natural numbers.
2. Is 0 a natural number?
No, zero (0) is not a natural number. Natural numbers are fundamentally used for counting objects, which begins with 'one'. Zero represents the absence of a value, or a null value, and is therefore the starting point for the set of whole numbers, not natural numbers.
3. What is the difference between natural and whole numbers?
The key difference lies in the inclusion of zero (0). Natural numbers begin at 1 and extend to infinity (1, 2, 3...). Whole numbers include zero and all the natural numbers (0, 1, 2, 3...). Therefore, all natural numbers are whole numbers, but not all whole numbers are natural numbers.
4. What are the properties of natural numbers?
Natural numbers possess several important properties under addition and multiplication:
- Closure Property: The sum and product of two natural numbers is always a natural number.
- Associative Property: The grouping of numbers doesn't affect the sum or product.
- Commutative Property: The order of numbers doesn't affect the sum or product.
- Distributive Property: Multiplication distributes over addition and subtraction.
5. Why are natural numbers also called 'counting numbers'?
Natural numbers are called 'counting numbers' because they are the numbers we use to count objects. When you count items, you start with 1, 2, 3, and so on. This direct application to the act of counting is why they're called 'counting numbers'.
6. Can a natural number be a fraction or a decimal?
No, a natural number cannot be a fraction or a decimal. By definition, natural numbers are whole integers. They do not have fractional or decimal parts. For instance, while 5 is a natural number, numbers like 5.5 or 1/2 (one-half) are not.
7. How are natural numbers used in everyday life?
Beyond simple counting, natural numbers are used for ordering (like ranking), in systems like barcodes (check-digit systems), and in various other applications requiring whole number sequences.
8. What are the first ten natural numbers?
The first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
9. What is the smallest natural number?
The smallest natural number is 1.
10. What are some examples of natural numbers?
Examples of natural numbers include 1, 2, 3, 10, 25, 100, 1000, and so on. Essentially, any positive whole number is a natural number.
11. Are all whole numbers natural numbers?
No, not all whole numbers are natural numbers. While all natural numbers are whole numbers, the number zero (0) is a whole number but not a natural number.
12. Are all natural numbers integers?
Yes, all natural numbers are integers. Integers include all whole numbers (positive and negative) and zero. Since natural numbers are positive whole numbers, they are a subset of the integers.
