Even Numbers: We live in a numerical world. We utilize numbers in our daily lives. We use numbers to buy something, make payments, ask about the price of something when playing games, the number of runs scored by the Indian team during a cricket match, to notice and count the number of birds perched on a tree, and so on. Mathematicians rely heavily on numbers. In primary school, we learned how to count numbers.

Even numbers are numbers or integers that are divisible by two. Even numbers include numbers such as 2, 4, 10, 24, 36, and so on. An odd number is one that is not divisible by two. On this page, we’ve covered all there is to know abo

ut Even Number, including a definition, an even number chart, and sample problems. Continue reading to learn more about Even Numbers.

Numbers and Types

Numbers are the building blocks of mathematics. These can be used to count or measure something. It has a very important role in our daily life and mathematics.

Examples of numbers are \(2,\;5,\;37,\;98,\; \ldots ..\) etc.

The number chapter is very vast. The numbers can be categorized as:
a) Natural Numbers \(\left( N \right)\)
b) Whole Number \(\left( W \right)\)
c) Integer \(\left( Z \right)\)
d) Rational and Irrational Numbers \(\left( Q \right)\)
e) Real Number \(\left( R \right)\)

Another way of classifying the numbers is the prime number and composite number. And, the other way of classifying the numbers are the odd numbers and even numbers.

Among all these types of numbers, the natural numbers \(\left(N \right)\), whole number \(\left( W \right)\) and integer \(\left( Z \right)\) involves both even and the odd numbers, which is the main concept to be discussed in this article.

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What is Even Number?

All the integers that are exactly divisible by \(2\) are called even numbers. Even numbers end with the digits \(0,\;2,\;4,\;6\) and \(8.\) Even numbers are multiples of \(2.\) The smallest positive even number is \(0.\) Even numbers can be both positive and negative.
Examples of even numbers are \( – 6,\; – 44,\;52,\;98,\;120\) etc.

Even Numbers Chart from 1 To 100

The chart of even numbers from \(1\) to \(100\) is given below. All the even numbers are coloured in orange and all the odd numbers are coloured in yellow.

 

What is an Odd Number?

An odd number is a number which is not divisible by \(2.\) When we divide any odd number by \(2,\) it leaves a remainder \(1\) always. Positive odd numbers are started from \(1\) i.e., \(1\) is the first positive odd number. Every alternative number from \(1\) are the odd numbers. It is not the multiple of \(2.\)

Practice Exam Questions

Even and Odd Numbers

Any number (natural number, whole number, integer) that cannot be divisible by \(2\) is called an odd number. When we divide an odd number by \(2\), it leaves the remainder as \(1\) always. Examples of some odd numbers are \(11,\;173,\;107,\;979\) etc. Odd numbers end with the digits \(1,\;3,\;5,\;7\) and \(9.\)

Any number (natural number, whole number, integer) divisible by \(2\) without leaving any remainder is called an even number. Examples of even numbers are \(2,\;72,\;422,\;38\) etc. Even numbers end with the digits \(0,\;2,\;4,\;6\) and \(8.\)
We can better understand the concept of even and odd numbers by the below flow chart,

Even and odd numbers are available on both sides of the number line. This means that even and odd numbers are both positive and negative. At the right side of the number line, every alternative number from \(0\) are a positive even number and every alternative number from \(1\) are a positive odd number. Similarly, at the left side of the number line, every alternative number from (0) is a negative even number, and every alternative number from (- 1) is a negative odd number.

Representation of Even and Odd Numbers on the Number Line

Even and odd numbers are available on both sides of the number line. This means the even and odd numbers are both positive and negative. At the right side of the number line, every alternative numbers after \(0\) are positive even numbers and every alternative numbers from \(1\) are positive odd numbers.

 

Similarly, at the left side of the number line, every alternative numbers from \(0\) (excluding \(0,\) because \(0\) is considered as a neither positive nor negative even number) are negative even numbers and every alternative numbers from \(- 1\) are negative odd numbers.

Formulae

Formula for Even Numbers

\(2n\) where \(n \in Z\) (Integer)

 

Formula for Odd Number

\(2n + 1\) where \(n \in Z\) (Integer)

How to Identify Even and Odd Numbers?

There are two methods of identifying whether a number is even or odd. They are:

1. By comprehending the digit of the number at units place:

The numbers having units place digit \(0,\;2,\;4,\;6\) and \(8\) are the even numbers.
Example: \(12,\;234,\;57378,\;9810\) etc.

Hundreds	Tens	Units
\(2\)	\(3\)	\(4\)

As the digit at the units place of the number \(234\) is \(4\) (even number), the given number is an even number. The numbers having units place digit \(1,\;3,\;5,\;7\) and \(9\) are the odd numbers.
Example: \(25,\;287,\;57371,\;9819\) etc.

 

Hundreds	Tens	Units
\(2\)	\(8\)	\(7\)

As the digit at the units place of the number \(287\) is \(7\) (odd number), the given number is an odd number.

2. By grouping:

As two items or numbers form a pair,

1. If we divide a number into groups of pairs, no element will be left in the case of even numbers.
2. But, in the case of odd numbers, one element will always be left after making pairs.

Addition of Even and Odd Numbers

Let us perform the addition of different combinations of even and odd numbers to see how the result (sum) is changing:

Number\(1\)	Number\(2\)	Sum
Even \(\left( 6 \right)\)	Even \(\left( 2 \right)\)	Even \(\left( {6 + 2 = 8} \right)\)
Odd \(\left( 9 \right)\)	Odd \(\left( 7 \right)\)	Even \(\left( {9 + 7 = 16} \right)\)
Even \(\left( 4 \right)\)	Odd \(\left( 1 \right)\)	Odd \(\left( {4 + 1 = 5} \right)\)
Odd \(\left( 3 \right)\)	Even \(\left( 4 \right)\)	Odd \(\left( {3 + 4 = 7} \right)\)

Let us summarize the above result through the picture,

Properties of Even Numbers

Let us have a look at the different properties of even numbers on operations like addition, subtraction, and multiplication:

Property of Addition

If two even numbers are added, an even number is obtained.
Example: \(12 + 24 = 36\)

If two odd numbers are added, an even number is obtained.
Example: \(3 + 5 = 8\)

If we add one even number and one odd number (and vice-versa), an odd number is obtained.
Example \(1\): \(8 + 3 = 11\)
Example \(2\): \(5 + 2 = 7\)

Property of Subtraction

The difference between two even numbers results in an even number.
Example: \(98 – 2 = 96\)

 

The difference between two odd numbers results in an even number.
Example: \(11 – 7 = 4\)

 

The difference between an even and an odd number (and vice-versa) results an odd number.
Example \(1\): \(10 – 3 = 7\)
Example \(2\): \(11 – 2 = 9\)

 

Property of Multiplication

The product of two even numbers result an even number.
Example: \(8 \times 4 = 32\)

 

The product of two odd numbers results an odd number.
Example: \(3 \times 7 = 21\)

 

The product of an even number and an odd number (and vice-versa) results an even number.
Example \(1\): \(10 \times 3 = 30\)
Example \(2\): \(5 \times 4 = 20\)

Division of Even and Odd Numbers

As observed above, there are a couple of rules existing that define the result of addition, subtraction, and multiplication of (i) two even numbers, (ii) two odd numbers, and (iii) an even number and an odd number. In all those cases, the result is always an integer.

But when we divide a number with another one, several different kinds of outcomes may be obtained.

(i) Division of an even number with another even number may result in a fraction or a decimal.
Example \(1\): Both \(2\) and \(10\) are even numbers. But \(\frac{2}{{10}} = \frac{1}{5} = 0.2.\) So, the result is a fraction or a decimal.

 

(ii) Division of an even number with another even number may result an integer.
Example \(2\): Both \(10\) and \(2\) are even numbers. But \(\frac{{10}}{2} = 5.\) So, the result is an integer.

 

(iii) The division of two odd numbers is an odd number when the denominator is a factor of the numerator.
Example \(3\): \(33 \div 3 = 11.\) Here, \(3\) is a factor of \(33.\) Here, \(11\) is an odd number.

 

(iv) The division of two odd numbers may be a fraction or a decimal number (terminating or non-terminating), if the denominator is not a factor of the numerator.
Example \(4\): Both \(9\) and \(15\) are odd numbers. But \(\frac{9}{{15}} = \frac{3}{5} = 0.6\) So, the result is a fraction or a terminating decimal.
Example \(5\): Both \(7\) and \(3\) are odd numbers. But \(\frac{7}{3} = 2.333333 \ldots \ldots.\) So, the result is a fraction or a non-terminating decimal.

Fun Facts about Even and Odd Numbers

1. Every alternative number in counting starting from \(2\) are even numbers and each alternative number starting from \(1\) are odd numbers.

2. \(0\) is neither a positive nor negative even number.

3. First positive even prime number is \(2\)

4. There are no common elements between even numbers and odd numbers set.

Consecutive Even Numbers

Suppose \(n\) is an even number, then the number \(n\) and \(n + 2\) are grouped under the category of consecutive even numbers.
Example: suppose \(4\) (the value of \(n\) is an even number, then \(n + 2 = 4 + 2 = 6\) (even number)
So, \(4\) and \(6\) are two consecutive even numbers.

Solved Examples on Even Numbers

Question-\(1\): Is \({\rm{8902648}}\) an odd number or even number?
Answer: As the number \({\rm{8902648}}\) ends with the digit \(8,\) it is an even number.

Question-\(2\): Is \({\rm{89763}}\) an odd number or even number?
Answer: As the number \({\rm{89763}}\) ends with the digit \(3,\) it is an odd number.

Question-\(3\): When we divide \(3009763789\) by \(2,\) what will be the remainder?
Answer: Here, the unit digit of the number \(3009763789\) is \(9.\) So, we can conclude that the given number is an odd number. We know that when an odd number is divided by \(2,\) we always get \(1\) as the remainder. Hence, when we divide \(3009763789\) by \(2,\) the remainder will be \(1.\)

Question-\(4\): Is \(67\) odd or even?
Answer: \(67\) is an odd number. As it ends with the digit \(7.\)

Question-\(5\): How many even numbers are there from \(1\) to 100
Answer: There are \(50\) even numbers from \(1\) to \(100.\)

Question-\(6:\) Are the following numbers even?
a. \(80 – 24\)
b. \(10 + 5\)
c. \(22 \div 11\)

Solution:
a. \(80 – 24 = 56,\) divisible by \(2.\) So, it an even number.
b. \(10 + 5 = 15,\) not divisible by \(2.\) So, it is an odd number.
c. \(22 \div 11 = 2,\) As \(2\) is divisible by \(2.\) So, it is an even number.

 

Question-\(7\): Is 1 an odd or even number?
Answer: \(1\) is an odd number. As it is not divisible by \(2.\)

 

Question-\(8\): What is the even number from \(1\) to \(100\)

Answer: The list of even numbers from \(1\) to \(100\) are,
\(2,\;4,\;6,\;8,\;10,\;12,\;14,\;16,\;18,\;20,\;22,\;24,\;26,\;28,\;30,\;32,\;34,\;36,\;38,\;40,\;42,\;\)
\(44,\;46,\;48,\;50,\;52,\;54,\;56,\;58,\;60,62,\;64,\;66,\;68,\;70,72,\;74,\;76,\;78,\;80,\;82,\;\)
\(84,\;86,\;88,\;90,\;92,\;94,\;96,\;98,\;100.\)

Question-\(9\): Is \(-22\) an even number?
Answer: Yes, as \(-22\) is divisible by \(2.\) It is an even number.

Related Topics to Study

1. Real Numbers 2. Whole Numbers 3. Odd Numbers 4. Irrational Numbers 5. Complex Numbers

Summary

The concept of Numbers is vast in Mathematics. In this article, we have covered even numbers and some concepts of odd numbers, the relation between even and odd numbers with some solved examples.

FAQs on Even Numbers

Below are the frequently asked questions on Even Numbers: 

Q.1. Write any two consecutive even numbers?
Ans: \(28\) and \(30\) are two consecutive even numbers. There are many such pairs possible. 

Q.2. What is the smallest even number?
Ans: Smallest even numbers cannot be obtained as even numbers are \( \ldots ,\; – 3,\; – 2,\; – 1,\;0,\;1,\;2,\;3,\; \ldots\). However, \(2\) is the smallest positive even number.

Q.3. Which is the odd number?
Ans: Odd numbers are whole numbers that cannot be divisible by \(2.\) When we divide any odd number by \(2,\) it leaves the remainder \(1\) always. Odd numbers end with the digits \(1,\;3,\;5,\;7\) and \(9.\) Some examples of odd numbers in the sequence are \(1,\;3,\;5,\;7,\;9,\;11,\;13,\;15,\;17\) etc. 

Q.4. What is called an even number?
Ans: A number that is divisible by \(2\) and generates a remainder \(0\) is called an even number. Even numbers are the multiple of \(2.\)

Q.5. Are all whole numbers even?
Ans: No, the whole numbers which are divisible by \(2\) are called the even numbers. Examples, \(3,\;5,\;7,\; \ldots \) are not even numbers.

Q.6. Is \(0\) an even number?
Ans: Yes, \(0\) is an even number. As when we divide \(0\) by \(2,\) we get the quotient and remainder as \(0.\)

Q.7. How to know if a number is even or odd?
Ans: If the number ends with \(0,\;2,\;4,\;6\) and \(8\) then the number is called an even number and if the number ends with \(1,\;3,\;5,\;7\) and \(9\) then the number is called an odd number.

 

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