- An even number is any integer exactly divisible by 2, so it ends in 0, 2, 4, 6, or 8
- Zero is counted as even because it divides by 2 with no remainder
- The smallest positive even number is 2, and every even number can be written in the form 2k.
This article gives you a detailed account of even numbers and the concept behind them, so that it is easier to understand and build the basic idea.
What is meant by Even Numbers?
Integers that are exactly divisible by two are called even numbers. Every even number ends in 0, 2, 4, 6, or 8; for example, 56, 48, 536, 484, 16, 18, and 2 are all even because each divides by 2 with no remainder. In algebra, any even number can be written as 2k, where k is an integer.
Can you guess the smallest positive even number? It is 2. Now you may be wondering about the integers that are not divisible by 2. The integers that are not divisible by two are known as odd numbers.
For example, 3, 15, 25, 37, and 195 are odd numbers.
By now, I hope you have got the idea of how to recognize an even or odd number. Let us do a quick revision.
- If the number is even, its last digit must be 0, 2, 4, 6, or 8.
- If the number is odd, then its last digit must be 1, 3, 5, 7, or 9.
What Are the Properties of Even Numbers?
Even numbers follow clear parity rules under the four basic operations. Adding or subtracting two even numbers gives an even result, while an even and an odd number give an odd result. Multiplying any number by an even number gives an even product. Division is excluded because dividing integers can produce fractions, which have no parity.
Addition Property
i) When an even number is added to another even number, the result is always even.
- 2 + 4 = 6
- 4 + 12 = 16
ii) When an odd number is added to an even number, the result is always odd.
- 3 + 6 = 9
- 5 + 8 = 13
iii) When an odd number is added to another odd number, the result is always even.
- 7 + 3 = 10
- 11 + 11 = 22
Subtraction Property
i) When an even number is subtracted from an even number, the result is even.
- 8 - 4 = 4
- 12 - 2 = 10
ii) When an odd number is subtracted from an even number, the result is always odd.
- 8 - 3 = 5
- 12 - 5 = 7
iii) When an odd number is subtracted from another odd number, the result is always even.
- 7 - 5 = 2
- 13 - 11 = 2
Multiplication Property
i) When an even number is multiplied by an even number, the product is always even.
- 2 × 2 = 4
- 4 × 6 = 24
ii) When an odd number is multiplied by an even number, the result is always even.
- 3 × 2 = 6
- 5 × 6 = 30
iii) When an odd number is multiplied by an odd number, the result is always odd.
- 3 × 5 = 15
- 7 × 3 = 21
Division Property
When you divide, the result may be a fraction, and fractions can never be classified as even or odd.
For example, when you divide two whole numbers such as 1 divided by 3, the result is one-third, which cannot be classified as odd or even. This is because only integers can be classified as odd or even, not fractions. Hence, there is no parity property for division.
How Can You Practice Identifying Even Numbers?
The best way to master even numbers is to practise sorting and adding them. Try identifying even numbers from a mixed list, listing even numbers within a range, and summing the first few even numbers. Regular practice with these short exercises builds speed and confidence in recognising parity at a glance.
Here is an exercise that will help you get the idea and concept of even numbers clearly, so that you can solve any sum related to even numbers easily.
- Which of the following numbers are even? 3, 4, 9, 15, 24, 34, 39, 45, 48, 315, 416, 7280
- Write all the even numbers that are greater than 60 and smaller than 70.
- Find the sum of the first five even numbers.
So now I hope you have a clear idea of what even numbers are. In short, even numbers can be divided into two equal halves, unlike odd numbers.