Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. For example, 2, 4, 6, 8, 10 and so on. Suppose you have 10 candies. These candies can be equally divided into two groups with 5 candies in each group. Hence, 10 is an even number. However, this grouping cannot be done for 11 candies, so 11 is not an even number. In this page, we will explore more interesting ways to understand even numbers, their properties, and interesting facts about them.
|1.||What Are Even Numbers?|
|2.||Odd and even numbers|
|3.||Properties of Even Numbers|
|4.||FAQs on Even Numbers|
Table of Contents
- What Are Even Numbers?
- Odd and even numbers
- Properties of Even Numbers
- FAQs on Even Numbers
- Solved Examples
- Practice Questions
What are Even Numbers?
An even number is a number that is a multiple of 2. Suppose John has 6 balls. If he tries to group them, he can pair all the 6 balls and form 3 pairs. There are no balls that are left unpaired. Therefore, he can conclude that 6 is an even number. Now, let’s divide 6 by 2. We get the quotient as 3, which is equal to the number of pairs that are formed. We get the remainder as 0, which is equal to the number of balls that cannot be paired. Whenever John tries to pair an even number of balls, he will be left with NO ball. In other words, whenever an even number is divided by 2, we will always get the remainder as 0.
Odd and Even Numbers
Let us go through a list of all the even numbers from one to two hundred. Observe the numbers given below. Can you find a pattern or a connection between all the even numbers from one to two hundred?
|List of Even Numbers (1-200)|
Let us perform addition on different combinations of odd numbers and even numbers and see the results. We will see how numbers change from odd to even when odd and even numbers are added to each other. Keep a note of the results that you get.
|Number 1||Number 2||Sum|
|4 [Even]||8 [Even]||12 [Even]|
|7 [Odd]||3 [Odd]||10 [Even]|
|1 [Odd]||6 [Even]||7 [Odd]|
|2 [Even]||9 [Odd]||11 [Odd]|
Let us summarize the result:
Properties of Even Numbers
Let us have a look at the different properties of numbers like addition, multiplication, and subtraction and the way an even number behaves in such cases:
Property of Addition
- The sum of two even numbers is an even number. For example, 14 + 8 = 22
- The sum of an even number and an odd number is an odd number. For example, 8+9=17
- The sum of two odd numbers is an even number. For example, 13+7=20
Property of Subtraction
- The difference between two even numbers is an even number. For example, 42-8=34
- The difference between an even number and an odd number is an odd number. For example, 22-7=15
- The difference between two odd numbers is an even number. For example, 35-15=20
Property of Multiplication
- The product of two even numbers is an even number. For example, 12 × 4 = 48
- The product of an even number and an odd number is an even number. For example, 8 × 5 = 40
Solved Examples on Even Numbers
Example 1: Mark has 30 pencils. He distributed 14 of those among his friends. Will he have an even number of pencils left? How do you know?
Mark distributed 14 pencils out of 30 pencils, so he had 16 left with him because 30 - 14 = 16. Since 16 is a multiple of 2, therefore, it is an even number.
Example 2: Tim recycled 45 newspapers and his friend recycled 38 newspapers. Is the total number of recycled newspapers an even number?
Add the number of newspapers recycled by Tim and his friend. 45 + 38 = 83. Tim and his friend recycled 83 newspapers in all. Since 83 is not divisible by 2, it is not an even number.
FAQs on Even Numbers
What are the Even Numbers from 1−100?
The list of even numbers from 1-100 is as follows: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60,62, 64, 66, 68, 70,72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100.
What is the Smallest Even Number?
2 is the smallest even number. It is also the only even prime number.
What is the Formula of Even Numbers?
Since every even number is a multiple of 2, therefore, its formula is given as n = 2k, where k is an integer. If we subsitute 'k' by any number, we get an even number. For example, if 'k' is replaced by 3 in 2k, (2×3) = 6. We get 6 which is an even number.
Is 0 an Even Number or an Odd Number?
Any number which can be divided by two to give another whole number is considered to be even. Zero is also one of them because when 0 is divided by 2, it gives the remainder 0, which means 0 is divisible by 2. Hence, 0 is an even number.
Why is 4 an Even Number?
Since 4 is a multiple of 2 and it can be divided into two equal groups, it is an even number. In other words, it as an even number because it is completely divisible by 2.
What is the Formula for Odd Numbers?
The formula for odd numbers is 2k + 1, where k is an integer. If we subsitute 'k' by any number, we get an odd number. For example, if k is replaced by 4 in 2k + 1, (2×4) + 1=9. We get 9 which is an odd number.