From Zero to One: Understanding the Concept of the Smallest Whole Number

# From Zero to One: Understanding the Concept of the Smallest Whole Number

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Vikram Singh
Assistant Manager - Content
Updated on May 14, 2024 15:43 IST

Unlock the mystery of the smallest whole number with this comprehensive guide. From its definition to its properties, this article will reveal everything you need to know about this tiny but mighty number.

If you’re reading this blog, you’re probably not just interested in the smallest whole number – you’re likely exploring the concept of whole numbers more broadly. In this article, we’ll briefly discuss what whole numbers are, their properties, and at the end, we’ll also touch on the concept of the smallest whole number.

So, without further delay, let’s dive into the article.

Table of Content

## What is a Whole Number?

A Set of Natural Numbers (1, 2, 3, 4, 5, 6, ….) including 0 are called Whole Numbers. In simple terms, it is a set of positive integers including zero.

Example: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10…….

Representation: W

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### Which is the Smallest Whole Number?

0 is the smallest whole number since the whole number starts with 0. On the number line, it lies between positive and negative integers.

## Properties

Let a, b, and c be whole numbers, then:

#### Closed under Addition and Multiplication

The sum or product of two whole numbers is a whole number.

i.e., a + b and a*b is a whole number.

Example:

(i). 4 + 2 = 6

(ii). 4 * 2 = 8

#### Associative Property

The sum or product of two whole numbers is always the same irrespective of groupings.

i.e.

(i). a + (b + c) = (a + b) + c

(ii). a * (b * c) = (a * b) * c

Example:

(i). 2 + (3 + 4) = 9 = (2 + 3) + 4

(ii). 2 * (3 * 4) = 24 = (2 * 3) * 4

#### Distributive Property

Multiplication is distributive over addition.

i.e. a * (b + c) = a * b + a * c

Example

2 * (3 + 4) = 2 * 7 = 14

2 * (3 + 4) = 2 * 3 + 2 * 4 = 6 + 8 = 14

=>  2 * (3 + 4) = 2 * 3 + 2 * 4

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#### Commutative Property

Sum or product of two numbers remains the same, even if you interchange the positions.

i.e.,

(i). a + b = b + a

(ii). a * b = b * a

Example:

(i). 2 + 3 = 5 = 3 + 2

(ii). 2 * 3 = 6 = 3 * 2

#### Identity Property

Additive identity: 0 is the additive identity, i.e., if you add any whole number with 0, then the result will be the same whole number.

In simple terms, a + 0 = a = 0 + a.

Example: 2 + 0 = 2 = 0 + 2

Multiplicative Identity: 1 is the multiplicative identity, i.e., if you multiply any whole number with 1, then the result will be the same whole number.

In simple terms, a * 1 = a = 1 * a

Example: 2 * 1 = 2 = 1 * 2

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## Additional Information on Whole Number

### Prime Number and Composite Number

The whole number consists of a prime number and a composite number, so let’s have a look at these numbers:

#### Prime Number:

A whole number greater than 1 that has only two factors, 1 and itself is known as a prime number.

Example: 2, 3, 5, 7, 9

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#### Composite Number:

A composite number greater than 1 that has more than one or more than one factor, i.e., it can be written as the product of two whole numbers.

Example:

8 = 2 * 2 * 2

15 = 3 * 5

35 = 5 * 7

So, the whole number can be a prime number or a composite number.

### Factor and Multiples

#### Factor:

A factor of a whole number is a whole number that divides the original number without leaving any remainder.

Example: Factors of 12 are 1, 2, 3, 4, 6, and 12. Since each number can divide into 12 without leaving any remainder.

#### Multiples:

A multiple of the whole number is a whole number that can be obtained by multiplying the original number by another whole number.

Example: Multiple of 3 are 3, 6, 9, 12, 15…

3 * 1 = 3, 3 * 2 = 6, 3 * 3 = 9, 3 * 4 = 12, 3 * 5 = 15

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## Conclusion

Whole numbers are the union of natural numbers and zero. Since, whole number starts from 0, so 0 is the smallest whole number. In this article, we have briefly discussed what is whole numbers, smallest whole number, properties of whole numbers with examples.

Hope you will like the article.

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## FAQs

What is a Whole number?

A whole number is a positive integer with 0, that doesn't have any fractional or decimal part.

Which is the smallest whole number?

0 is the smallest whole number.

Is zero a whole number?

Yes, zero is a whole number.

What is the difference between natural number and whole number?

All natural numbers are whole number, But all whole numbers are not natural number. in simple terms, natural numbers are subset of whole numbers.

Can a whole number be negative?

No, whole number can't be negative. Since, it is the union of natural number and zero.

What is the largest whole number?

There is no largest whole number, there are infinitely many whole numbers.