 # Even and Odd Numbers

How do you count the number of subjects in which you get homework? You do it by counting from 1 and then go on. The natural way of counting is 1, 2, 3 and so on. How will you say when you do not get any homework on any subjects?  You will say zero. In this section, we will study different types of numbers. We will discuss natural numbers, whole numbers, odd and even numbers.

### Suggested Videos        ## 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. ### 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

The numbers which are divisible by 2 are even numbers. Even numbers leave 0 as a remainder when divided by 2. Even numbers have 0, 2, 4, 6 or 8 as their unit digit. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 etc. are even numbers. The sets of even number are expressed as Even = {2n: n ∈ integer (number)}.

Is 0 an even number? Zero is an even number as it is a multiple of 2. It can be expressed as {2n = 2 × 0}.

## 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. Think of any two odd numbers. Subtract the two odd numbers. What do you get? An even number? Multiply the two odd numbers? What is the product? An odd number. Repeat this with any other odd numbers. The result will be the same. This shows that the product of any two odds is an odd number. When we subtract any two odd numbers, we get an even number.

## Solved Example for You

Problem: Is 134256791 an even number?
Solution: The unit digit of the given number is 1 which is odd. The above number will leave 1 as a remainder when divided by 2. The number 134256791 is odd.

Problem: What is the sum of two even numbers? What is the sum of two odd numbers?
Solution: The sum of two even numbers is always an even number. Two odd numbers add up to give an even number.

Question: What are even numbers?

Answer: Even numbers refer to an integer then we can divide by two and it remains an integer or has no remainder. However, an integer that is not an even number is an odd number. Also, even the number that is not positive can be integers too.

Question: State the first non-negative even number?

Answer: The answer is zero because it is the first non-negative even number, while two is the first positive even number. Zero is the first non-negative integer because we can divide it by two without any difficulty.

Question: Explain what is a mystery number?

Answer: Mystery number refers to a number that we can express as a sum of two numbers and those two number should be reverse of each other. For example, 23 and 32 can be a mystery number because they are reverse of each other.

Question: Mention the even numbers in-between 1 and 50?

Answer: There are 25 even number between 1 and 50. These are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, and 50.  All the other remaining number in-between 1 and 50 are odd numbers.

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