# Natural Numbers, Even Numbers, Odd Numbers

13/07/2020

### Natural Numbers

The natural numbers are the counting numbers. It goes like 1, 2, 3, 4, …, and so on. It is interesting to know that if we subtract 1 from any natural number, we get its predecessor (previous number). If we add 1 to any natural numbers, it gives its successor (next number).

The predecessor of 5 is 5 − 1 = 4. The successor of 5 is 5 + 1 = 6. Is there any natural number that has no predecessor? The predecessor of 2 is 1. What is the predecessor of 1? Does that predecessor is also a natural number? No, no natural number is the predecessor of 1.

### Whole Numbers

Suppose you have 5 chocolates and you distribute them among your friends. How many chocolates do you have? Zero. Zero is denoted by the symbol 0. When we add 0 to the group of natural numbers, we get whole numbers. The predecessor of 1 is 1 − 1 = 0. 1 has the predecessor which is a whole number and not a natural number.

### 0 + Natural Numbers = Whole Numbers

#### Properties of Zero

• Any number, when multiplied by 0, gives 0.
• When 0 is added to any number, nothing changes.
• When 0 is subtracted from any number, it remains the same.
• 0 is the smallest whole number.

The whole numbers are said to consist of two types of numbers – even numbers and odd numbers.

### Even Numbers

A whole number exactly divisible by 2 is called even numbers.

For example:

2, 4, 6, 8, 10, 12, 14, 16……………………..are even number. Or a number having 0, 2, 4, 6, 8 at its units place is called an even number.

246, 1894, 5468, 100 are even number.

Any two even numbers which differ from one another by 2 are called consecutive even number.

### Odd Numbers

Odd numbers are the numbers which are not completely divisible by 2. The odd numbers leave 1 as a remainder when divided by 2. They have 1, 3, 5, 7, and 9 as their unit digit. 1, 3, 5, 7, 9, 11, 13, 15, etc. are odd numbers. The sets of odd number are expressed as Odd = {2n + 1: n ∈ integer (number)}.

#### Steps to Check for Odd and Even Numbers

• Divide the number by 2.
• Check the remainder.
• If the remainder is 0, it is an even number else if the remainder is 1, it is an odd number.

Check Odd & Even