Whole numbers are the set of natural numbers, including zero. They are denoted by the symbol “W” and are used to represent quantities that do not include fractional parts. Whole numbers have many properties that are similar to natural numbers, but they include zero as well, which has its own unique properties.

## Properties of Whole Numbers:

- Closure Property: The sum, product or difference of any two whole numbers is always a whole number.
- Commutative Property: The order of the whole numbers in addition and multiplication does not matter. For example, 2 + 3 = 3 + 2, and 2 x 3 = 3 x 2.
- Associative Property: The grouping of whole numbers in addition and multiplication does not matter. For example, (2 + 3) + 4 = 2 + (3 + 4), and (2 x 3) x 4 = 2 x (3 x 4).
- Distributive Property: Multiplication is distributive over addition. For example, a x (b + c) = (a x b) + (a x c).
- Identity Property: The sum of any whole number and zero is the same whole number, and the product of any whole number and one is the same whole number.
- Even and Odd Numbers: Even numbers are whole numbers that are divisible by 2, while odd numbers are not divisible by 2.
- Divisibility: A whole number is said to be divisible by another whole number if it can be divided exactly by that number without leaving a remainder. For example, 6 is divisible by 3 because 6 divided by 3 is 2 with no remainder.
- Prime Numbers: Prime numbers are whole numbers greater than 1 that are only divisible by 1 and themselves. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
- Composite Numbers: Composite numbers are whole numbers that are not prime, and are divisible by more than 1 and themselves. For example, 4, 6, 8, 9, 10, 12, and 14 are all composite numbers.
- Factors: Factors are the whole numbers that divide a given number exactly. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

## Applications of Whole Numbers:

Whole numbers and their properties are used in a wide range of applications in mathematics, science, and engineering. They are used to represent quantities, perform calculations, and solve problems. For example, whole numbers are used to represent the number of items in a collection, the size of a population, or the number of parts in a machine. They are also used in calculating distances, areas, and volumes in geometry, in analyzing data in statistics, and in designing electrical circuits.

## Summary

Whole numbers and their properties are fundamental concepts in mathematics. They are used to represent quantities that do not include fractional parts, and have many properties that are similar to natural numbers. Understanding these properties can help us perform calculations and solve problems in a variety of fields, and by mastering the properties of whole numbers, we can develop a strong foundation for further mathematical study and problem-solving in a range of contexts.