1. Even Numbers
Even numbers are those integers that can be divided into two equal groups and are exactly divisible by 2. For example, 12, 34, 46, 58, 110, etc. Suppose you have 12 burgers. You can divide these burgers into two groups with 6 burgers each. Hence, 12 is an even number. However, this grouping cannot be done for 13 burgers, so 13 is not an even number. In this article, we will explore more about even numbers, list them, and their properties.
1.1 How to know if the number is even or odd?
Any integer that can be exactly divided by 2 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.
- 8 – if we divide the given number 8 by 2 i.e 8 ÷ 2 then the remainder is 0. So, 8 is an even number.
- 14 – again if we divide the given number 14 by 2 i.e. 14 ÷ 2 then the remainder is 0. So, 14 is an even number.
- 15 – if we divide 15 by 2 i.e. 15 ÷ 2 then the remainder comes out as 1, so 15 is not an even number. It is an odd number.
- 17 – check this by the same method. You will find 17 ÷ 2 gives the remainder 1. So 17 is not an even number. It is an odd number.
But what if you are given very large numbers, say, 85647 and 954238? How to check if the given number is even or odd without dividing it by 2?
That particular number in one’s place will tell whether the number is odd or even.
- Even numbers end with 0, 2, 4, 6, 8
- Odd Numbers end with 1, 3, 5, 7, 9
For example, 85647 has 7 in one's place - So, 85647 is an odd number. 954238 has 8 in one’s place - So, 954238 is an even number.
Hence, summarising the concept of even numbers as follows:
1.2 List of even numbers from 1 to 100
| 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 |
1.3 Properties of Even Numbers
Following are the properties of even numbers including operations with odd numbers:
Addition property:
- The sum of an even number and odd number is an odd number. For example, 8 + 5 = 13
- The sum of two even numbers is an even number. For example, 6 + 4 = 10
Subtraction Property:
- The difference between an even number and an odd number gives an odd number. For example, 12 – 7 = 5
- The difference between two even numbers gives an even number. For example, 14 – 8 = 6
Multiplication Property:
- The multiplication of two even numbers gives an even number. For example, 6 x 4 = 24
- The multiplication of an even number and an odd number gives an even number. For example, 8 x 5 = 40
Division property:
If the two numbers do not divide exactly, the result of the division i.e. the quotient will not be a whole number, hence, will neither be even nor odd. However, when the two numbers divide exactly, we refer to the following properties:
- An even number divided by an even number may be even or may be odd. For example, 16 ÷ 4 = 4 and 18 ÷ 2 = 9
- An even number divided by an odd number is even. For example, 20 ÷ 5 = 4
An odd number cannot be divided by an even number to give a whole number. The quotient will be a decimal number, which is neither even nor odd. For example, 35 ÷ 10 = 3.5 which is neither an odd nor even number.
