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The Concept and Characteristics of Odd Numbers

Odd Numbers

The numbers which are not divisible by 2 evenly are termed odd numbers. Their division into two separate integers is not possible evenly. The remainder will always be found when an odd number is divisible by 2 or an even number. The common examples of odd numbers are 1, 3, 5, 7, and 9. Let’s know more about Odd Numbers Properties.

The opposites of even numbers are the odd numbers. They are also known as numbers that cannot be arranged in pairs. Generally, odd numbers are integer numbers that cannot be categorised into two parts equally. 

  • To understand odd numbers better, we can consider having fruits in even numbers and vegetables in odd numbers. 
  • We will find that the fruits which being even in numbers form a pair, whereas the vegetables which are odd in number do not form pairs entirely. 
  • The best way to find out whether the number is odd or even is to divide it by 2. If it is divisible by two, then it’s not an odd number and vice versa. 
  • Odd numbers always carry 1, 3, 5, 7, or 9 at their unit’s place, also keeping in mind that after dividing a particular number by 2, if the remainder is not zero, then the number is odd.

Below is the document the odd numbers from 1 to 1000 are mentioned, but it becomes interesting to know that none of the odd numbers is multiples of 2; out of the first 200 numbers, 100 numbers are odd.

 According to the Ancient Greeks, these numbers were considered as numbers that could not be managed in two rows as odds. However, this ancient greeks concept has gone through various changes over the millennia. 

The number which is not a multiple of 2 is commonly referred to as an odd number. We explain everything concerning the definition, examples, properties, and types of odd numbers in this topic.

Definition of Odd numbers

They are defined as numbers that are not divisible by two, for example, a number in form 2a + 2, where k  Z ( integers, i.e.) are called odd numbers. It is interesting to know that the numbers or integers can be either odd or even on a number line.

The difference between even numbers and odd numbers

The numbers which are divisible by two are not odd and are called the even numbers. The even numbers can be parted in two and divided equally, but the odd numbers cannot be parted in two numbers or divided equally.

The examples of which are 8, which is an even number that can be divided into four equal parts as 2-2-2-2, but 5 cannot be divided as it would result in a remainder of 1 by dividing it by 2.

The odd number chart from 1 to 100

This chart includes the odd numbers from 1 to 100, and referring to this chart, the odd numbers from 100 to a maximum can be found.

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

List of odd numbers

This list includes the number of odd numbers from 1 to 25, 26 to 50, 27 to 75, and 76 to 100. It is noted that among the count of 1000, there are five hundred odd numbers and five hundred even numbers.

Range of number Numbers of odd figures
1 – 25 12
26 – 50 12
51 – 75 12
76 – 100 12

The following table can be taken into consideration while counting the odd numbers irrespective of the figure.

Following is the general list of the odd numbers between the successive numbers ;

Odd numbers between 0 – 100

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,

71,73,7……………………………99

Odd numbers between 101 – 200

101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,…………….145,147,149,151,153,155,157,159,161,163,165,167,169,171,173,175,177,179,181,183,…………………….,199.

Odd numbers between 201 – 300

201,203,205,207,209,211,213,215,217,219,221,223,225,227,229,231,233,235,237,239,241,243,245,247,249,251,253,255,257,259,261,263,265,267,269,271,273,275,277,279,281,285,287,289……………….299.

Odd numbers between 301 – 400

301,303,305,307,309,311,313,315,317,319,321,323,325,327,329,331,333,335,337,339,341,343,345,347,349,351,353,355,357,359,361,363,365,367,369,371,373,375,377,379,381,383,385,387,389…………………,399.

Odd numbers between 401 – 500 

401,403,405,407,409,411,413,415,417,419,421,423,425,427,429,431,433,435,437,439,441,443,445,447,449,451,453,455,457,459,461,463,465,467,469,471,473,475,477,479,481,483,485…………………….499.

Odd numbers properties:

The Properties of odd numbers are related to their BODMAS operation, including multiplication, addition, division, and subtraction. With the help of this concept, can we come to a common answer for all of the number properties? 

Here, we have a set of properties that will be applied to any odd number you will ever come across, not only for 1 to 200. Here, we have the following properties that are discussed below.

1. Addition of two odd numbers-  

Any odd number when added to another odd number results in an even number.

Example: 5 (odd number) + 5 (odd number)  = 10 (even number) 

In this senario, 10 is divisible by even number as five parts of 2 ie.   

2+2+2+2+2=10.

2. Subtraction of two odd numbers – 

While subtracting an odd from an odd number, a result is always an even number. It is similar to the addition of odd numbers.

Example: 15 (odd number) – 13 (odd number) = 2 (even number)

Here, the answer is 2 as there is also an even number and divisible by 2.

3. Multiplication of two odd numbers – 

While multiplying an odd number with another odd number, the result we get is an odd number.

Example:  3 (odd number) x 3 (odd number) will be equal to 9 (odd number).

In this scenario, the result obtained is 9, which is an odd number and not divisible by 2.

4. Division of two odd numbers –  

The result obtained by dividing an odd number from another odd number is an odd number only when the denominator is a numerator factor. Otherwise, the number results in a decimal point number.

Example: 33 (odd number) ÷ 11 (odd number) will equal 3, which is again an odd number that cannot be divisible by 2.

The following chart can be referred to for summarising odd numbers:

Operation Result
Odd no. + odd no. Even no.
Odd no. – odd no. Even no.
Odd no. x Odd no. Odd no.
Odd no. / odd no.

  • Where the denominator is the factor of the numerator.
Odd no.

Types of odd numbers

There are two types of odd numbers :

  1. Consecutive odd numbers
  2. Composite odd numbers
  1. Considering ‘x’s as an odd number, adding +2 in ‘x’s would give us x and x + 2, called consecutive odd numbers.

Common examples are 5 and 7, 17 and 19.

  1. Composite odd numbers – multiplying two smaller positive integers or multiplying the number with one resulting in the formation of a positive integer is called a composite number. Examples of composite odd numbers are  15,21, 25, 27, 33, 35, 39, 45, 49 and so on.

As we learned about the odd numbers, let us have a look at the number zero. Is number zero an odd number?

The answer is no. Number Zero is considered as an even number as it can be divided by 2. This is due to the quotient equal to 0 and a 0 remainder, which is left after dividing 2 by 0.

Conclusion

Hope you now have a clear concept of odd numbers, their types and properties.

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