Algebra

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# Even Numbers

## The Definition of an Even Number

**An even number is an integer that can be divided by 2 without a remainder.**

An integer is a whole number. Examples of integers are 0, 5013, and -44. Examples of non-integers are 3/5, 1.3, and -√11.

Zero is an even number because it is an integer and has no remainder when divided by 2. For example, 0/2 = 0. It passes the test for being an even number.

All even numbers will have a last digit of 0, 2, 4, 6, or 8. The size of the number does not matter, it just needs to fulfill the rule that it is an integer and can be divided by 2 without a remainder.

Example of some positive even numbers shown with red background.

### Example Problems

**Problem 1:**

Is 20 an even number?

Solution:

1.) Let’s check if 20 is even by using both rules.

2.) The last digit is a 0 so we know it’s an even number. Also, 20/2 = 10. There is no remainder, so it is even.

3.) **Yes, 20 is an even number.**

**Problem 2:**

Is 31 an even number?

Solution:

1.) Let’s check if 31 is even by using both rules.

2.) The last digit is a 1 so we know it’s not an even number. Also, 31/2 = 15 R1. There is a remainder of 1, so it is not even.

3.) **No, 31 is not an even number.**