Even Numbers - Definition, Properties, Addition, Subtraction, Multiplication and Even and Odd Differences
 

What is an Even Number?

Any integer in the number system, which when divided by two yields no remainder, is said to be an even number. This implies that the numbers are even if they are exactly divisible by the number 2. The one-digit examples of even numbers are 2, 4, 6, and 8. The two-digit, three digits numbers etc., are even, if they contain 0, 2, 4, 6, and 8 in their unit’s place. All these numbers are even numbers because they leave no remainder on division with 2. The numbers which counter the even numbers are called odd numbers and are defined as the integers which leave some remainder on division with 2. They also yield a decimal value and are not perfectly divisible. Examples of such numbers are 3, 5, 13, 11, 21, etc.

Knowing Even Numbers Practically

Let us assume that Ram has 8 apples. If he groups them in pairs, he will have 4 pairs of apples with no apple left unpaired. That means the remainder is zero. From this, we can deduce that 8 is perfectly divisible by 2, with the quotient being 4. This experiment proves that if an even number is divided by 2, then the remainder will always be zero (no remainder left). Likewise, if he pairs them as 3 then he will form 2 groups of 3 apples, and 1 group will be left with 2 apples. This implies that 8 is not completely divisible by odd numbers. Even numbers are only multiples of 2.

Difference between Even and Odd

To inspect whether the numbers are either even or odd, we need to carefully check the unit’s place of the numbers. The numbers having 0, 2, 4, 6, and 8 as their unit digits will be called even numbers, while the numbers containing 1, 3, 5, 7, and 9 are considered as odd numbers. Let us consider a random number, say 315, since it has 5 in its unit place and 5 is an odd number; therefore, the number is also an odd number. Similarly, 11, 223, 877, and 69 are odd numbers.

Properties of Even Numbers

Even numbers share a lot of properties. Let us now learn about various arithmetic properties of even numbers such as addition, subtraction, etc.

Addition Property

• Even numbers add up to yield another even number. For example, 20 + 6 = 26
• The summation of an even number with an odd number always results in an odd number. For example, 2 + 11 = 13
• The addition of two odd numbers yields an even number. For example, 27 + 3 = 30

Subtraction Property

• Similar to addition, two even numbers subtract to form an even number. For example, 40 - 2 = 38
• The difference between an even number and odd number results in the formation of an odd number. For example, 19 – 2 = 7.
• Subtracting an odd number with another odd number gives an even number. For example, 41 – 11 = 30

Multiplication Property

Two even numbers multiplied by each other yields an even number, and the product of an even and an odd number is also an even number. For example, 4 * 6 = 24, 3 * 8 = 24.