Even Numbers: Definition, Properties and FAQ – Mindspark

Even Numbers: Introduction

Any number which is completely divisible by 2 is an even number. In other words, if we divide a number by 2 and it leaves no remainder, then the number is an even number. On the other hand, if the number leaves a remainder then the given number is odd.

Let us check some numbers if they are even or odd:

1. 2 – If we divide the 2 by 2, then the remainder is 0. Hence, the given number 2 is an even number.
2. 16 – If we divide the given number 16 by 2, the remainder is 0. So 16 is an even number.
   
3. 15 – Dividing 15 by 2 (15÷ 2) leaves 1 as a remainder. So 15 is not an even number but an odd number.

Know If a Given Number is Even or Not Without Dividing it By 2.

You can divide small numbers by 2 to check if the number is even or not. But dividing large numbers can be time-consuming. So you should know the trick to identify if the number is even or not without dividing it by 2.

For this, you should check the ones place or unit digit of the given number. If the ones place of a given number has digits 0, 2, 4, 6 and 8, then the given number is an even number. Otherwise, the given number is odd.

Let’s check these two numbers- (1) 7249910 and (2) 2091311.
You can now clearly see that in the first number, 7249910, the unit digit is 0. So, 7249910 is even.
For the second number, 2091311, the unit digit is 1. So, 2091311 is odd.

This is the way you can check any number for even or odd.

Properties of Even Numbers

Let’s have a look at the different properties of even numbers like addition, subtraction, and multiplication.

Addition

1. The sum of two even numbers is also an even number. For example, 16 + 6 = 22.
   
2. The addition (sum) of an even number with an odd number is always an odd number. For example, 8 + 9 = 17.

Subtraction

1. The difference (subtraction) of two even numbers is again an even number. For example, 42 – 10 = 32.
   
2. The subtraction (difference) of an even number and an odd number is always an odd number. For example, 22 – 9 = 13.

Multiplication

1. The product (multiplication) of two even numbers is always an even number. For example, 13 × 4 = 52.
   
2. The product (multiplication) of an even number and an odd number is always an even number. For example, 8 × 7 = 56.

Examples

1. Identify even numbers from the given set of numbers- 13, 8, 92, 17, 32, 143, 500.

Solution:

8, 92, 32 and 500 are even since their last digits are 8, 2, 2 and 0, respectively, and this is the identification of an even number.

2. Write the first ten positive even numbers.

Solution:

2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 are the first ten positive even numbers.