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Difference Between Odd And Even Numbers, Properties, Important Topics For JEE 2024

Difference Between Odd And Even Numbers : Read everything you need to know about the numbers. Learn about the difference between odd and even numbers and their properties.

Shrivastav 17 Jan, 2024

Difference Between Odd And Even Numbers : The difference between odd and even numbers may be stated in terms of their general forms. Odd numbers and even numbers are two key types of numbers in mathematics that students learn in their early education.

Even and Odd Numbers are separate sets of whole numbers that are classified as odd or even according to specified features. Even numbers are precisely divisible by two, but odd numbers are not. The even and odd numbers are grouped alternately in the number system. It should be noted that a number cannot be both even and odd. There is a considerable difference between odd and even numbers .

Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams! Before we discuss the properties and difference between odd and even numbers, let’s first learn their meanings.

Even Number Definition

Even numbers are those that, when divided by two, leave zero as the remainder. An integer is considered even if it is perfectly divisible by two, leaving zero as the remainder. The last digit of an even number is always going to be 0, 2, 4, 6, or 8, thus we can recognize even numbers by keeping this in mind.

How are Even numbers to be identified?

By looking at the digit at the "ones" place

Using this method, we determine if an integer is even or odd by looking at the value in the "ones" place. Every integer that ends in 0, 2, 4, 6, and 8 is an even number. Even numbers include, for instance, 14, 26, 32, 40, and 88.

By Dividing

A number is even if it can be divided into two groups with the same number of elements in each.

Properties of an Even Number

Look at the addition, multiplication, and subtraction properties of even numbers.

Addition Property

An even number can be obtained by adding two even numbers. As an example, 12 + 8 equals 20.
An odd number is equal to an even number plus an odd number. As an example, 6 + 7 equals 13.
An even number can be obtained by adding two odd numbers. As an example, 15 + 11 equals 26.

Subtraction Property

An even number can be obtained by subtracting two even numbers. As an example, 32 – 6 = 26.
An odd number is the result of subtracting an even number from an odd number. As an example, 37 – 4 = 33.
An even number is obtained by subtracting two odd integers. As an example, 63 – 17 = 46.

Multiplication Property

An even number is created when two even numbers are multiplied. As an example, 14 x 2 equals 28.
An even number becomes an odd number multiplied by an even number. As an example, 10 x 3 equals 30.
An odd number can be obtained by multiplying an odd integer by another odd number. As an example, 3 x 5 equals 15.

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Odd Number Definition

Odd numbers in mathematics are those that have a remainder of one when divided by two. When a number is divided by two and the remaining amount is one, the number is said to be odd. The method for recognizing odd numbers is to use the simple fact that their final digit is always one of these: 1, 3, 5, 7, or 9. It may be expressed as 2n+1, where n is any whole number.

Difference Between Odd and Even Numbers

We have learned what even and odd numbers are. We will now learn the difference between odd and even numbers. The following table lists the basic difference between odd and even numbers :

Difference Between Odd and Even Numbers
Property	Odd Numbers	Even Numbers
Definition	Numbers with a remainder of 1 when divided by 2	Numbers with a remainder of 0 when divided by 2
Representation (Mathematical)	Can be expressed as 2n + 1, where n is an integer	Can be expressed as 2n, where n is an integer
Examples	81, 35, 55, 7, etc.	98, 26, 48, 6, 8, etc.
Last Digit Pattern	Ends with 1, 3, 5, 7, or 9	Ends with 0, 2, 4, 6, or 8
Product of Two Numbers	The product is always an odd number	The product is always an even number
Sum of two Numbers	The sum is always an even number	The sum is always an even number
Prime Number Property	Odd numbers (except 1) are prime numbers	Even numbers (except 2) are non-prime numbers

Difference Between Odd and Even Numbers FAQs

Q1: How do you know if a number is odd or even?

Ans. A number is divided by 2 to find out whether it is even or odd. A number is considered to be even if the remainder left behind after division is zero.

Q2: How do you compare odd and even numbers?

Ans. The number is even if its last digits are 2, 4, 6, 8, or 0. A number is odd if its last digit is one of the following: 1, 3, 5, 7, or 9.

Q3: Is 0 an even or odd number?

Ans. The number zero is even. To show that zero is even, one may easily verify that it meets the criteria for "even", which is an integer multiple of two, particularly 0 × 2.

Q4: Which is the smallest even number?

Ans. 2 is the smallest even number. Also, it is the only even prime number and the smallest prime number.

Q5: Is -2 even or odd?

Ans. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

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Even Number Definition

How are Even numbers to be identified?

By looking at the digit at the "ones" place

By Dividing

A number is even if it can be divided into two groups with the same number of elements in each.

Properties of an Even Number

Look at the addition, multiplication, and subtraction properties of even numbers.

Addition Property

An even number can be obtained by adding two even numbers. As an example, 12 + 8 equals 20.
An odd number is equal to an even number plus an odd number. As an example, 6 + 7 equals 13.
An even number can be obtained by adding two odd numbers. As an example, 15 + 11 equals 26.

Subtraction Property

An even number can be obtained by subtracting two even numbers. As an example, 32 – 6 = 26.
An odd number is the result of subtracting an even number from an odd number. As an example, 37 – 4 = 33.
An even number is obtained by subtracting two odd integers. As an example, 63 – 17 = 46.

Multiplication Property

An even number is created when two even numbers are multiplied. As an example, 14 x 2 equals 28.
An even number becomes an odd number multiplied by an even number. As an example, 10 x 3 equals 30.
An odd number can be obtained by multiplying an odd integer by another odd number. As an example, 3 x 5 equals 15.

Looking For Best Books for the JEE Exam Preparation?

Odd Number Definition

Difference Between Odd and Even Numbers

We have learned what even and odd numbers are. We will now learn the difference between odd and even numbers. The following table lists the basic difference between odd and even numbers :

Difference Between Odd and Even Numbers
Property	Odd Numbers	Even Numbers
Definition	Numbers with a remainder of 1 when divided by 2	Numbers with a remainder of 0 when divided by 2
Representation (Mathematical)	Can be expressed as 2n + 1, where n is an integer	Can be expressed as 2n, where n is an integer
Examples	81, 35, 55, 7, etc.	98, 26, 48, 6, 8, etc.
Last Digit Pattern	Ends with 1, 3, 5, 7, or 9	Ends with 0, 2, 4, 6, or 8
Product of Two Numbers	The product is always an odd number	The product is always an even number
Sum of two Numbers	The sum is always an even number	The sum is always an even number
Prime Number Property	Odd numbers (except 1) are prime numbers	Even numbers (except 2) are non-prime numbers