Odd Numbers

# Odd Numbers

Odd numbers are the numbers categorized as the non-multiples of 2. That precisely means that odd numbers are defined as those that cannot be divided by 2 evenly, i.e., odd numbers cannot be divided into two separate integers evenly. If an odd number is divided by 2, then that odd number will leave a remainder.
Examples of odd numbers are 1, 3, 5, 7, etc.
Also, we must note that Odd numbers are the exact opposite concept of even numbers.

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## What are Odd Numbers?

If you are wondering what numbers are, read the article below. Odd numbers are defined as the number which cannot be divided by two evenly.
Odd numbers can be represented as 2k+1, where k ∈ Z (i.e. integers). Also, the numbers existing on a number line can either be categorized as odd numbers or even numbers.

### Odd Numbers and Even Numbers

The even numbers are the numbers which are divisible by 2. Odd numbers cannot be divided into two parts evenly but even numbers can be divided evenly on dividing the number by 2.
For example, 4 can be divided and paired into two parts as 2-2, but 3 cannot be divided and paired. Hence, 4 is even and 3 is an odd number.

Below mentioned are a few points about odd numbers.
An odd number is not a multiple of 2
When divided by 2, odd numbers leave a remainder.
On the number line, 1 is the first positive odd number

### Odd Numbers 1 to 100 Chart

Below mentioned table is the chart of all the odd numbers from 1 to 100. Students must write and learn the odd numbers 1 to 100 on their notebooks. Students can also print the below given chart of odd numbers for their revision.

 1 11 21 31 41 51 61 71 81 91 3 13 23 33 43 53 63 73 83 93 5 15 25 35 45 55 65 75 85 95 7 17 27 37 47 57 67 77 87 97 9 19 29 39 49 59 69 79 89 99

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### List of Odd Numbers

The number of odd numbers in the following number range is mentioned below.

 Number Range No. of Odd Numbers 1 to 50 25 1 to 100 50 1 to 200 100 1 to 300 150 1 to 500 250 1 to 1000 500 1 to 10000 5000

### Properties of Odd Numbers

The properties of odd numbers is discussed below.

Any odd number added to another odd number always gives an even number.
Odd + Odd = Even number

#### Subtracting Two Odd Numbers

When an odd number is subtracted from an odd number, the result will be the even number.
Odd – Odd = Even number

#### Multiplication of Two Odd Numbers

If two odd numbers are multiplied then the number obtained will always be an odd number.
Odd × Odd = Odd number

#### Division of Two Odd Numbers

Division of two odd numbers always results in an odd number. The only condition is that the denominator must be a factor of the numerator, or else the number results in a decimal point number.
Odd ⁄ Odd = Odd number

### Consecutive Odd Numbers

If ‘a’ is an odd number, then ‘a’ and ‘a + 2’ are called consecutive odd numbers.
Below mentioned are examples of consecutive odd numbers.
15 and 17
29 and 31
-5 and -3
-13 and -11 and more.

### Solved Examples on Odd Numbers

Example 1: Find the sum of the smallest and the largest 2 digits odd numbers and also prove that it is divisible by 2.
Solution:
Smallest 2 digit odd number = 11
Largest 2 digit odd number = 99
Sum of both the numbers = 11 + 99 = 110
The number 110 is divisible by 2.
This proves that the number is even.Example 2: Is the following number odd number or even?
22 – 27
Solution: 22 – 27 = -5, is an odd number

Example 2: Is the following number odd number or even?
22 – 27
Solution:

22 – 27 = -5, is an odd number

## Frequently Asked Questions on Odd Numbers

### What is meant by odd numbers?

Odd numbers are integers that cannot be evenly divided by 2. When divided by 2, odd numbers leave a remainder of 1. Odd numbers can be represented as 2k + 1, where k is an integer.

### What are the first 10 odd numbers?

The first 10 odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

### Is zero an odd number? Why?

No, zero is not an odd number. It doesn't fit the definition of odd numbers or even numbers. Odd numbers leave a remainder of 1 when divided by 2, but zero divided by 2 results in a remainder of 0. Therefore, zero is not considered odd number or even number.

### What are the odd numbers from 1 to 100?

The odd numbers from 1 to 100 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ..., 99.

### What is the sum of all odd numbers from 1 to 100?

The sum of all odd numbers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series. With 50 odd numbers in this range, the sum is calculated as: Sum = 50/2 * (1 + 99) = 25 * 100 = 2500. Therefore, the sum of all odd numbers from 1 to 100 is 2500.

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