An integer is an odd number if it is not evenly divisible by 2, that is, it yields a remainder of 1 when divided by 2.

20,201,024,180,205,169 is odd since it's not divisible by 2: remainder = 1 when divided by 2. An integer is odd if its last digit is: 1, 3, 5, 7, or 9. Odd = {2 × k + 1, where k ∈ Z}

Operating rules:

The following rules apply when operating with even and odd numbers:

Adding: even + even = even; even + odd = odd; odd + odd = even.

Subtracting: even - even = even; even - odd = odd; odd - odd = even.

Multiplying: even × even = even; even × odd = even; odd × odd = odd.

An integer is called an even number if it is divisible by 2; in other words, an integer is called an even number if there is no remainder when dividing it by 2.

An integer is called an odd number if it is not divisible by 2, in other words, if there is a remainder of 1 when dividing it by 2.

If a number is even then it is not an odd number.

The property of an integer of being either even or odd is called parity.

Examples of even and odd numbers:

Even numbers: -14, 2, 0, 8, 56, and 127388 (there is no remainder when divided by 2).

Odd numbers: -13, 1, 5, 97, 19, and 127387 (all leave a remainder of 1 when divided by 2). All prime numbers except number 2 are odd numbers.

Hint: an integer number is even or odd according to whether its last digit is even or odd: if the last digit is 0, 2, 4, 6, or 8, then it is even, otherwise it's odd.

Formal definition of even and odd numbers:

An even number, "a", can be always written as the product of 2 and other integer, "k": "a = 2 × k";

As a result, an odd number, "b", since it leaves a remainder of 1 when divided by 2, can be always written as the product of 2 and other integer, "k", plus 1: "b = 2 × k + 1";

Practical application

(In some countries) Have you noticed that in regard to street house numbering, they are labeled so that the houses on one side of the street have even numbers and on the other side they have odd numbers?