Natural Numbers, Even Numbers, Odd Numbers

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