Odd and Even Numbers

Even and Odd Numbers are distinct groups of whole numbers that are classed as odd or even based on specific properties. Even Numbers are those which are exactly divisible by 2 on the other hand Odd Numbers are those that are not exactly divisible by 2. The even and odd numbers are arranged alternatively in the number system. It should be pointed out that no number can be both even and odd.

There exists a significant difference between the even and the odd numbers. In this article, we will learn about what are even and odd numbers and what is the difference between odd and even numbers in detail.

What are Even Numbers?

Even numbers are those numbers whenever divided by two will result in zero as the remainder. If we are given a number and if it is exactly divisible by 2 i.e. gives zero as the remainder then it is an even number. We can identify even numbers by remembering that the last digit of an even number will always be 0, 2, 4, 6, or 8.

For example : 98, 26, 48, 6, 8, and so on are all even numbers. Even numbers can be negative such as  -98, -26, -48, and so on.

Even Number Examples

Even numbers are integers that have a remainder of zero when divided by two. It has the form 2n, where n can be any integer.

There are an infinite number of even numbers, hence it is impossible to list them all. However, we may list the first even numbers, which contain both positive even numbers like 2, 4, 6, 8, 10, and so on, going to infinity, and negative even numbers like -2, -4, -6, -8, -10, and so on, reaching to negative infinity. Furthermore, 0 is an even number since it is divided by two (2 divides 0 with a residual of 0).

What are Odd Numbers?

In mathematics, odd numbers are numbers which when divided by two result a remainder as one. If we are given a number and divide it by two and will result in the remainder is one, then it is an odd number. The approach to identifying odd numbers is that the odd number’s last digit is always 1, 3, 5, 7, or 9. It can be written in form of 2n+1 , where n can be any integer number.

For example : 81, 35, 55, 7, and so on are all odd numbers. Odd numbers can also be negative, as in -81, -35, -55, and so on.

Odd Number Examples

There are an infinite number of odd numbers, hence it is impossible to list them all. However, we may list the initial odd numbers, which contain both positive odd numbers like 1, 3, 5, 7, 9, and so on, going to infinity, and negative odd numbers like -1, -3, -5, -7, -9, and so on, reaching to negative infinity.

Properties of Even and Odd Numbers

While performing the operations with odd and even numbers we can observe some trend in the result. These trends result in the properties of the even number and odd numbers. The properties of odd and even numbers are tabulated in the table below:

Properties	Example
Even + Even = Even	4 + 2 = 6
Even + Odd = Odd	6 + 3 = 9
Even – Even = Even	12 – 10 = 2
Even – Odd = Odd	8 – 3 = 5
Even × Even = Even	6 × 2 = 12
Even × Odd = Even	8 × 3 = 24
(Even)n = Even	(2)5 = 32
Odd + Odd = Even	7 + 3 = 10
Odd + Even = Odd	3 + 4 = 7
Odd – Odd = Even	9 – 7 = 2
Odd – Even = Odd	13 – 4 = 9
Odd × Odd = Odd	9 × 3 = 27
Odd × Even = Even	7 × 4 = 28
(Odd)n = Odd	(3)4 = 81

Difference between Odd and Even number

We have learnt what are even and odd numbers. Now we will learn the differences between odd and even numbers. The differences between odd and even numbers are tabulated below:

Odd Numbers	Even Numbers
Odd numbers are numbers which when divided by two result a remainder as one.	Even numbers are those numbers whenever divided by two will result in zero as the remainder.
It can be written in form of 2n+1 , where n can be any integer number.	It can be written in form of 2n, where n can be any integer number.
81, 35, 55, 7, and so on are all odd numbers	98, 26, 48, 6, 8, and so on are all even numbers.
The approach to identifying odd numbers is that the odd number’s last digit is always 1, 3, 5, 7, or 9.	We can identify even numbers by remembering that the last digit of an even number will always be 0, 2, 4, 6, or 8.
The product of two odd numbers is always an odd number.	The product of two even numbers is always an even number.
The sum of even number of odd numbers is always an even number.	If we add even numbers irrespective of times then their sum will always an even number.
Odd Numbers are Prime Numbers except 1	Even Numbers are non-prime numbers except 2.

Tips on Even and Odd Numbers

1. In counting numbers, all alternate number beginning with 1 is an odd number; for example, 1, 3, 5, 7, 9, 11, 13, and so on are odd numbers.
2. Similarly, any alternative number beginning with 2 is an even number; for example, 2, 4, 6, 8, 10, 12, and so on.
3. Checking a number’s divisibility by 2 is a simple approach to determine if it is even or odd.
4. Non-integer numbers, such as 1/2, 0.88, or infinity, are neither even nor odd.

Read More,

• Prime Numbers
• Arithmetic Operations
• Rational Numbers

Solved Examples on Even and Odd Numbers

Example 1: Tory has 5 green apples. Tory has one yellow apple more than the total number of green apples she already has. Is the total number of yellow apples and green apples Tory has an even number or odd number?

Solution:

Tory has five green apples. The number 5 can not be evenly divided by the number 2. This means that the number of green apples Tory has is an odd number.

The number of yellow apples she has is one more than the total number of green apples. In other words,

Total number of yellow apples = 5 + 1 = 6 apples

The number 6 can be evenly divided by the number 2. This means that the total number of yellow apples Tory has is an even number.

Example 2: Determine whether the following numbers are even or odd,

• 23
• 2 + 4 + 6 + 8 + 12
• 99 – 67

Solution:

Here ,23 is not divisible by 2, so it is an odd number

Sum of even numbers is 2 + 4 + 6 + 8 + 12 = 32. Since 32 is divisible by 2, it is not an odd number, so it is an even number

95 – 67 = 28. Since 28 is divisible by 2, it is not an odd number, so it is an even number

Thus, here only 23 is an Odd Number .

Example 3: How many even numbers are between 1 and 200?

Solution:

Out of all integers, half of them are even and half of them are odd. So, there are 200 integers between 1 and 200 (including 1 and 200), so half of them are odd and half of them are even.

Thus, there are 100 even number between 1 and 200.

Example 4: Find the product of all odd numbers between 1 to 10.

Solution:

The Odd numbers between 1 to 10 are 1, 3, 5, 7, and 9.

The product of all odd numbers between 1 to 10 = 1 * 3 * 5 * 7 * 9 = 945.

Thus, product of all odd numbers between 1 and 10 is 945.

Example 5: Write any 10 consecutive odd numbers between 1 and 50.

Solution:

As every other number in a continuous series of natural numbers is odd number.

So, 1, 3, 5, 7, 9, . . ., 49 is the list of all odd numbers between 1 and 50.

Thus, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 or 21, 23, 25, 27, 29, 31, 33, 35, 37, 39 are some of the examples of 10 consecutive odd numbers between 1 and 50.

Practice Questions on Odd and Even Numbers

Q1. How many Even and Odd Numbers are between 1 to 50?

Q2. Find the sum of first 5 odd numbers

Q3. Find the sum of first 5 even numbers

Q4. Verify that sum of two even number is always even

Q5. Check if product of a odd and even number is even or odd.

FAQs on Odd and Even Numbers

1. What are Odd and Even Numbers?

In simple words, odd numbers are those integers that can’t be divided evenly by 2 (e.g., 1, 3, 5), while even numbers are those integers that can be divided by 2 without a remainder (e.g., 2, 4, 6).

2. How can you identify whether a number is Even or Odd?

If a number is divided by two and the remainder is zero, it is an even number; otherwise, it is an odd number.

3. Identify whether the difference between two Odd Numbers will be even or odd ?

Yes, the difference between two odd numbers will always be an even number. For example : 63 and 35 are two odd numbers, where the difference 63 – 35 = 28 which is even number.

4. Is the difference of two Even Numbers even or odd?

Yes, the difference between two even numbers will always be even. For example : 76 and 32 are two even numbers, where the difference 76 – 32 = 44 which is even number.

5. Are Decimal Numbers considered to be Even or Odd?

Decimals cannot be classed as even or odd since they are not whole numbers. The same may be said of fractions.

6. Is it possible that all Even Numbers are Natural Numbers?

No, not every even number is a natural number. Integers that are even but not natural numbers, such as -2, -4,-6, and so on, are all even but not natural numbers.