Natural Numbers: Definition, Examples, Properties & Whole Number

Natural Numbers: Natural numbers are the numbers we use for counting, like 1, 2, 3, etc. So, what are natural numbers in simple words? They are the first numbers we learn in schools.

Learning what are natural numbers helps kids understand how to count objects, such as toys, pencils, stars, or steps.

You may wonder, what are natural numbers in maths exactly? Well, whenever you count your chocolates or the number of friends you have, you're using natural numbers. These numbers are very important in learning basic math and help make math fun and exciting!

By understanding natural numbers, kids can solve simple math problems and learn more complex math later. Natural numbers make math fun and help us see patterns in the world around us!

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Natural Numbers Definition

Let’s learn the natural number definition. Natural numbers are the numbers that begin from 1 and go on without an end. These numbers are called “counting numbers” too.

Natural numbers are the basic numbers we use for counting. Natural numbers are an infinite list of numbers that start with 1. Natural numbers are the positive whole numbers: 

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

Important Things About Natural Numbers:

1. Positive whole numbers : Natural numbers are always positive (not negative or zero).
2. Counting numbers : They are the numbers you use when you count things, like counting apples or people.
3. No fractions or decimals : Natural numbers do not include fractions or decimal numbers.
4. No end : You can keep counting forever. There's always a number after any number you say.

So, when someone asks, what are natural numbers, you can tell them: “They are numbers like 1, 2, 3, 4... and so on.”

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Natural Numbers Examples

Natural numbers are the fundamental numbers we use for counting. They start from 1 and continue infinitely. Here are some examples of natural numbers:

• Single-digit numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9
• Multi-digit numbers: 10, 23, 456, 7890, 123456
• Large numbers: 1000, 1000000, 1000000000 (one billion)

This natural numbers list keeps going forever. So, if someone asks, “Can you tell me the natural numbers list?”, you can start from 1 and just keep counting! This is why we say natural numbers are infinite.

Natural Numbers 1 to 100

The natural numbers from 1 to 100 are the first 100 whole numbers used for counting. Here they are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

These are all natural numbers, starting from 1 and going up to 100.

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Properties of Natural Numbers

Natural numbers are the set of positive integers, starting from 1 and extending infinitely. They are denoted by the symbol N. The following are the fundamental properties that govern the arithmetic operations on natural numbers:

1. Closure Property

A set is closed under an operation if applying that operation to elements in the set always produces a result within the same set.

• Addition : The sum of any two natural numbers is always a natural number. Example: 2 + 3 = 5, which is a natural number.
• Multiplication : The product of any two natural numbers is always a natural number. Example: 4 × 5 = 20, which is a natural number.

Note: Natural numbers are not closed under subtraction or division.

2. Commutative Property

An operation is commutative if changing the order of the operands does not change the result.

• Addition : The order of numbers in addition does not affect the result. Example: 3 + 4 = 4 + 3.
• Multiplication : The order of numbers in multiplication does not affect the result. Example: 5 × 6 = 6 × 5

This works for addition and multiplication, but not for subtraction or division.

3. Associative Property

An operation is associative if the grouping of operands does not change the result.

• Addition : The grouping of numbers in addition does not affect the result. Example: (2 + 3)+ 4 = 2+ (3 + 4)
• Multiplication : The grouping of numbers in multiplication does not affect the result. Example: (2 × 3) × 4 = 2 × (3 × 4).

4. Distributive Property of Multiplication over Addition

This property states that multiplication distributes over addition.

• Multiplication distributes over addition . Example: 2 × (3 + 4) = (2 × 3) + (2 × 4).

All of these properties help us understand what are natural numbers in maths and how they work in everyday math. They form the basis for more complex mathematical reasoning and problem-solving.

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Is 0 a Natural Number?

0 is not considered a natural number in the traditional sense. Natural numbers are usually defined as positive whole numbers starting from 1, like 1, 2, 3, and so on. In this case, 0 is not included.

In modern mathematics, there are two common ways to define natural numbers:

1. Natural numbers as positive whole numbers : This older definition doesn't include 0.
2. Natural numbers as whole numbers that are not negative : This definition includes 0 and positive whole numbers.

But mostly, we say natural numbers start from 1. So, for your schoolwork, remember that what are natural numbers usually means 1, 2, 3, and so on.

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Natural Numbers and Whole Numbers

Natural numbers and whole numbers are both sets of numbers used in counting and basic math operations, but they have a few key differences. Natural numbers start from 1 and go on infinitely, while whole numbers start from 0 and go on infinitely.

In short, natural numbers start from 1 and are used for counting, while whole numbers include zero along with the natural numbers. Both sets of numbers are used in everyday situations, but whole numbers are often more practical when zero is involved, like in measurements or inventories.

Why Do We Learn Natural Numbers?

You might be wondering, why do we even need to learn natural numbers? Well, here’s why:

• To count our toys, friends, or days of the week

• To solve basic math problems

• To understand more about shapes, money, and time later

So the next time someone asks, what are natural numbers, you’ll know they are the building blocks of all maths we do.