# You are given two numbers a and b you have to find the number which is divisible by a and b

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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. These numbers can be grouped in equal pairs. However, this grouping cannot be done for numbers like 5, 7, 9, or 11. So, 5, 7, 9, or 11 are not even numbers. Let us learn more about even numbers and their properties in this page.

## What are Even Numbers?

An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number. This can be understood with the help of an example. Suppose John has 6 balls. If he tries to group them, he can pair all 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 us 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

Whole numbers can be classified into even and odd numbers. Odd numbers are those numbers that are not completely divisible by 2. Whereas, even numbers are completely divisible by 2. 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)
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
102 104 106 108 110
112 114 116 118 120
122 124 126 128 130
132 134 136 138 140
142 144 146 148 150
152 154 156 158 160
162 164 166 168 170
172 174 176 178 180
182 184 186 188 190
192 194 196 198 200

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 Number 1 + Number 2 = Sum
4 [Even] 8 [Even] 4 + 8 = 12 [Even]
7 [Odd] 3 [Odd] 7 + 3 = 10 [Even]
1 [Odd] 6 [Even] 1 + 6 = 7 [Odd]
2 [Even] 9 [Odd] 2 + 9 = 11 [Odd]

Let us summarize the result.

### Consecutive Even Numbers

Consecutive numbers can be listed as 2, 4, 6, 8, 10, 12, 14, and so on. Consecutive numbers are those numbers that follow each other in order continuously from the smallest number to the largest number. For example, 1, 2, 3, 4, and so on are consecutive natural numbers. So, when we need to list consecutive even numbers, we can list all even numbers in order from the smallest number to the largest number. For example, 2, 4, 6, 8, 10, 12, 14, and so on are consecutive even numbers.

### Even Natural Numbers

Even natural numbers can be listed as 66, 24, 8, 100, and so on. Even numbers are those numbers that are divisible by 2 and natural numbers are counting numbers that start from 1, 2, 3, 4, 5 and so on. So, if we pick all the even numbers from the list of natural numbers they will be called even natural numbers.

## 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 of Even Numbers

• 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 of Even Numbers

• 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 of Even Numbers

• 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

## Even Prime Numbers

There is only one even prime number which is 2. All the other even numbers have factors other than 1 and the number itself. For example, the factors of 4 are 1, 2, and 4. Hence, there is only one even prime number which is 2.

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1. 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?

Solution:

Mark distributed 14 pencils out of 30 pencils, so he had 16 left with him because 30 - 14 = 16. We know that 16 is a multiple of 2, thus, it is an even number. Therefore, he will have an even number of pencils left, that is 16.

2. Example 2: State true or false with reference to even numbers.

a.) The only even prime number is 4.

b.) All even numbers are composite numbers.

Solution:

a.) False, the only even prime number is 2.

b.) False, all even numbers are not composite numbers, 2 is an even number but it is not a composite number. It is a prime number because 2 has only two factors, 1 and 2 itself.

3. Example 3: Select the even numbers from the following:

a.) 778

b.) 912

c.) 223

Solution:

a.) 778 is an even number because it is divisible by 2.

b.) 912 is an even number because it is divisible by 2.

c.) 223 is not an even number, it is an odd number because it is not divisible by 2.

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## FAQs on Even Numbers

Numbers that are completely divisible by 2 are termed as even numbers. These numbers when divided by 2 leave 0 as the remainder. For example, 2, 4, 6, 8, and so on are 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.

### Are all the Even Numbers Natural Numbers?

Yes, all the even numbers that are completely divisible by 2 are also natural numbers. For example, 14, 18, 22, 24, etc.

### 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 substitute '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 is an even number because it is completely divisible by 2.

### What is the Difference Between Odd Numbers and Even Numbers?

An even number is a number that is a multiple of 2. For example, whereas an odd number is not a multiple of 2.

### What is the HCF of Two Consecutive Even Numbers?

The HCF of two consecutive even numbers is 2. The Highest Common Factor (HCF) of any two numbers is their highest common factor. For example, 16 and 18 are two consecutive even numbers and their HCF is 2.

### How to Find an Even Number?

In order to find an even number, we should divide the given number by 2. If it is completely divisible by 2 without leaving any remainder, then it is an even number. If the given number is not completely divisible by 2, it is an odd number.

### What are the Even Numbers less than 10?

Even numbers less than 10 can be listed as 2, 4, 6, and 8. These numbers are completely divisible by 2 without any remainder.

### What are Even Composite Numbers?

Even numbers are those numbers that are completely divisible by 2. For example, 2, 4, 6, 8, 10, and so on are even numbers. Composite numbers are those numbers that have factors more than 1 and the number itself. For example, 4, 6, 9, 15, and so on. We know that all even numbers, except 2, have factors more than 1 and the number itself. Interestingly, 2 is the only even number that is considered to be a prime number. Therefore, except 2, all even numbers are composite numbers. For example, 4, 6, 8, 10, 12, 14, and so on, are even composite numbers. This also shows that the smallest even composite number is 4.

### What is the Largest 4 Digit Even Number?

The largest 4-digit even number is 9998. We know that the largest 4-digit number is 9999, so, the first even number after that is 9998.

### What is the Sum of 2 Consecutive Even Numbers?

The sum of 2 consecutive even numbers is always an even number. For example, 4 + 16 = 20 or, 66 + 12 = 78 and so on.