Odd Numbers

“Odd numbers’ ‘ are regarded as those that have the remainder 1 after dividing from 2.  According to ancient Greeks, odd numbers cannot be arranged in two rows. For example, except for all the multiples of the 2 are odd numbers. The simple definition of the odd numbers is that 1 in their remainder if “divided” by two are an “odd number”.

Definition

The definition of the “odd numbers” is that they cannot be divided into two equal parts that are 1, 3, and 5. etc.  Let’s assume for example shoes and slippers, the shoes contain the numbers like 1, 3, and 5. On the other side, the slippers are 2, 4, and 6. Hence, the odd numbers do not create the pair entirely, one of them remains unfair. However, even numbers contain the pair of slippers in all sequences. The even numbers can be divided into two different equal parts.

Properties of odd numbers

The arithmetic operation on the odd numbers comes to the conclusion. The set of their properties does not apply for the numbers from 1-100, however, it is applicable for the entire list of the odd numbers. The list of the properties is given below that is applicable for all “odd numbers”.

Addition

The addition of the 2 “odd numbers” is consistently an “even number” means the ad of two “odd numbers” consistently gives an “even number”. As example, 5 (odd) +7 (odd) =12 (even), 1001(odd) + 1003 (odd) = 2004 (even).

Subtraction

The minus of the 2 “odd numbers” consistently gives an “even number”. AS example 7 (odd) – 5 (odd) = 2 (even), 2003 (odd) – 1001(odd) = 1002 (even).

Multiplication

If there is, the multiplication of the 2 “odd numbers” always gives an “odd number”. As an example, 3 (odd) × 7 (odd) = 21 (odd).

Division

If there is a division of two “odd numbers” consistently gives an “odd number”. As an example, 21 (odd) ÷ 7 (odd) = 3 (odd).

Arithmetic operation”	Results
“Odd number + Odd number”	“Even number”
“Odd number – Odd number”	“Even number”
“Odd number × Odd number”	“Odd number”
“Odd number ÷ Odd number”	“Odd number”

Categories of “odd numbers”

“Consecutive Odd Numbers”

In the finding of “consecutive odd numbers”, if n is the “odd number” and the sum of n+2 is also an “odd number” and the group is known as “Consecutive odd numbers”. The difference between the consecutive odd numbers will always be 2. For example, 3 and 5, 11 and 13 and so on.

“Composite Odd Numbers”

Composite means it is made from many parts. These odd numbers can be formed by the simple multiple of two or more “odd numbers”. Multiple of the “odd numbers” gives the “odd number”. There are some examples of “composite odd numbers” that are among 1 to 25 are “9, 15, 21, 25”.

“Odd and even numbers”

The odd numbers cannot be divided equally, the one part always be greater than the other parts however the even numbers are divided into two equal parts. All the “even numbers” are multiples of two or that can be divided by 2 and two different equal’s parts are obtained. Odd numbers cannot be divided by 2 and remain 1 reminder after dividing from 2 then that number is the odd number and one part is always greater than the other. The difference between the odd and even numbers helps to understand the odd numbers; it is difficult to understand the odd number without the discussion of even numbers.

“Even numbers”	“Odd numbers”
Are divisible by 2 and leave the remainder zero	When divided by 2 leaves remainder 1
Number is the multiple of 2	Number is not the multiple of 2
The last digit of the numbers consists 0,2,4,6,8	The last digit of the numbers consists 1,3,5,7,9
They can be groped in the pair	They cannot be grouped in the pair

Odd numbers 1 to 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	75	77	79
81	83	85	87	89	91	93	95	97	99

Conclusion

At the end of this article, it can be seen that an “odd number” has “1, 3, 5, 7 or 9” in their unit place. They are not divisible by 2 and obtain 1 in their remainder when divided by 2. They are not in the pair and the last one does not get their pair. The different types of odd numbers are discussed in the article. The difference between the even and the odd numbers is discussed. Without comparing with even numbers it is difficult to understand odd numbers