Odd numbers are numbers that cannot be arranged in pairs i.e., all integers except the multiples of 2 are odd numbers. If we divide an odd number by 2, then it will leave a remainder. For example: 11, 13, 29, 55, etc. Odd numbers are just the opposite concept of even numbers.
Any integer that cannot be completely divided by 2, and leaves a remainder is called an odd number.
Let’s see some examples and check if the number is odd or not.
But what if you are given very large numbers, say, 35647 and 954238? How to check if the given number is odd or even without dividing it by 2?
That particular number in one’s place will tell whether the number is odd or even.
For example, 35647 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 odd numbers as follows:
1 | 3 | 5 | 7 | 9 |
11 | 13 | 15 | 17 | 19 |
21 | 23 | 25 | 27 | 29 |
31 | 33 | 35 | 37 | 39 |
41 | 43 | 45 | 47 | 49 |
51 | 53 | 55 | 57 | 59 |
61 | 63 | 65 | 67 | 69 |
71 | 73 | 75 | 77 | 79 |
81 | 83 | 85 | 87 | 89 |
91 | 93 | 95 | 97 | 99 |
Following are the properties of odd numbers including operations with even numbers:
Addition Property:
Subtraction Property:
Multiplication Property:
Division Property:
If the two numbers do not divide exactly, i.e. the quotient will be a decimal value and not a whole number, hence, will neither be even nor odd. However, when the two numbers divide exactly, we refer to the following properties:
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