Even Numbers


Any number which is exactly divisible by 2 is called an even number. i.e. if a number when divided by 2 leaves no remainder, then the number is called an even number.

If the number when divided by 2 leaves a remainder then the number is an odd number.

Let’s see some examples and check if the number is even or not.

  1. 2 – if we divide the given number 2 by 2 i.e 2 ÷ 2 then the remainder is 0. So the given number 2 is an even number.

  2. 10 – again if we divide the given number 10 by 2 i.e. 10 ÷ 2 then the remainder is 0. So the given number 10 is an even number.

  3. 5 – if we divide 5 by 2 i.e. 5 ÷ 2 then remainder comes out as 1, so the given number 5 is not an even number. It is an odd number.

  4. 11 – check this by the same method. You will find 11 ÷ 2 gives remainder 1. So 11 is not an even number. It is an odd number.

So, examples of Even numbers are :–  2, 4, 6, 8, 10, 12, 14, 42, 50, 98, 100 etc. 

How to Check if a Given Number is Even or Not Without Dividing it By 2.

A number can be checked if it is even or not without dividing it by 2. This can be done by just checking the units place of a given number. If the units place of a given number contains digits 0, 2, 4, 6 and 8. Then the given number is an even number.

  • Unit digit of Even number contains either of the following digits:  0, 2, 4, 6 or 8.

  • Unit digit of Odd number contains either of the following digits: 1, 3, 5, 7 or 9.

By this method, you can check if the given large number is Even or Odd. Let's consider two numbers- (1) 72580 and (2) 2311. You can now clearly check that in first number 72580 the unit digit is 0. So, 72580 is even. And for the second number 2311, the unit digit is 1. So, 2311 is odd.

List of Even numbers up to 100. 

There are 50 even numbers between 1 to 100. They are given in the below table.

2

12

22

32

42

52

62

72

82

92

4

14

24

34

44

54

64

74

84

94

6

16

26

36

46

56

66

76

86

96

8

18

28

38

48

58

68

78

88

98

10

20

30

40

50

60

70

80

90

100


Properties of Even numbers

  1. Property of Addition of Even Numbers

  1. Even + Even = Even

Eg.  12 + 14 = 26. 

       10 + 8 = 18.

  1. Even + odd = odd

Eg.  12 + 11 = 23. 

       10 + 7 = 17.


  1. Property of Subtraction of Even Numbers

a ) Even - Even = Even

Eg.  18 - 14 = 4. 

   10 - 4 = 6.

b ) Even - odd = odd

Eg.  12 - 11 = 1. 

  1. - 7 = 15.


  1. Property of Multiplication of Even Numbers

Even x Even = Even

Eg.  8 x 2 = 16. 

12 x 4 = 48.

Even x odd = Even

 Eg.  2 x 3 = 6. 

 8 x 7 = 56.


Solved Examples

Q1.  Choose even numbers from the given set of numbers. 11, 8, 91, 07, 31, 143, 500, 252, 581, 1794.

Ans

Even numbers are 8, 500, 252 and 1794.


Q2. Write first 10 even numbers.

Ans

2, 4, 6, 8, 10, 12, 14, 16, 18, 20.


Q3. What is the smallest even number?

Ans

2 is the smallest even number.


Q4. How can you check a given is Even or Odd?

Ans.

Unit digit of Even number is either 0, 2, 4, 6 or 8. While, Unit digit of Odd number is either 1, 3, 5, 7 or 9.   


Q5. What will be the resulting number (Even or Odd) for the following operations

  1. 67347 + 9846

  2. 58731 x 90754

  3. 11235 – 10110

  4. 23421 x 12895

  5. 99981 + 85789    

Ans.

A) odd B) Even C) odd D) odd E) Even