What is an odd number ?  Definition and examples.

An odd number is an integer that cannot be grouped in twos. For example, it is not possible to group 5 computers in groups of twos only. Therefore, 5 is an odd number. 

As you can see from the illustration above, an odd number is always going to have a remainder of 1 when you try to make groups of twos.

In the example above, there are two groups of two computers and a remainder of 1 computer. In other words, 5 = 2 × 2 + 1

7 will give you 3 groups of 2 and a remainder of 1 and we can write it as

7 =  2 × 3 + 1

9 is also an odd number and we can write it as 9 =  2 × 4 + 1

A negative integer can also be an odd number as long as you can show that there is a remainder of 1.

For example,  -5 = 2 × -3 + 1  and  -7 = 2 × -4 + 1

Do you see a pattern? The numbers in red do not change. The number in the middle is an integer.

The definition of odd numbers apply only to integers! It would not make sense to say that a fraction, a decimal, or a real number is an odd number.