# Multiples of 8

Introduction

Multiples are the number which divide the number completely without the remainder. Multiples are the product of a given number with an integer. For example we can say that multiples of 8 are the numbers obtained by the product of 8 with the natural numbers like 1, 2, 3, 4,….so on. Some of the multiples of 8 are 8, 16, 24, 32, 40, 48 and so on….It is impossible to list all multiples of 8, since there are an infinite number of natural numbers. In this article let us study all the multiples of 8 and how to determine multiples of 8.

### What are Multiples of 8?

The multiples of 8 are all the numbers that result from the multiplication of 8 by another whole number or an integer.Any number that can be represented as in the form of 8n , where n is considered as an integer and a multiple of 8.

It is said that an integer”n”is a multiple of the integer”m”if there is an integer”k”, such that n = m x k.

So to know multiples of 8, m = 8 must be substituted in the equation.

Therefore, n = 8 x k is obtained.

That is, multiples of 8 are all those numbers that can be written as 8 multiplied by some whole number. For example:

n  = 8 x 1, then 8 is a multiple of 8.

n = 8 * (- 3), then -24 is a multiple of 8.

### Multiples of 8 by Multiplication

To find the multiples of 8 we must be familiar with the multiplication table of 8. Multiples of 8 will be the product of 8 with any natural number i.e 8n, where n is any natural number.

Finding the Common Multiples of 8, We Can Write it as:

Writing the numbers from 8 to 0 in the following manner:

 8 6 4 2 0 8 6 4 2 0

Now, for the ten’s digit in each column in Row 1 will be written from 0 to 4 as:

 08 16 24 32 40 8 6 4 2 0

Similarly, we will write for the ten’s digit from 4 to 8 in Row 2 as:

 08 16 24 32 40 48 56 64 72 80

So, we get the first 10 multiples of 8 as:

08

16

24

32

40

48

56

64

72

80

Similary, the next 10 multiples of 8 are:

8  x 11 = 88

8  x 12 = 96

8  x 13 = 104

8  x 14 = 112

8  x 15 = 120

8 x 16 =  128

8 x 18 = 144

8 x 19 = 152

8 x 20 = 160

However, we have an easy trick to write the first 20 multiples of 8, which is as follows:

Write the numbers 8, 6, 4, 2, 0, writing 4 two times in the following manner:

 8 6 4 2 0 8 6 4 2 0 8 6 4 2 0 8 6 4 2 0

Now, write the numbers from 0 to 8 in the following manner:

 08 16 24 32 40 48 56 64 72 80

Now, from 8 to 16, writing 12 two times in the following manner:

 88 96 104 112 120 128 136 144 152 160

Now, joining these two boxes, we get the first 20 multiples of 8:

 08 16 24 32 40 88 96 104 112 120 48 56 64 72 80 128 136 144 152 160

From here, we concluded that the first multiple of 8 is 8 itself, the second one is just its double, i.e., 16, and the third is just the three times of 8, i.e., 8 x 3 = 24. Now, if I ask you to fill up the column to determine the nth multiple, let’s start this game:

1. 8, 24,____,56 ,_____,______,_________, 112

Here, we will do numbering from the first number till the last, including the blanks:

1 – 8

2 – 24

3- blank

4 – 56

5 – blank

6 – blank

7 – blank

8 – 112

We can observe the pattern as the first multiple is 8 x 1 = 8, the second is the third multiple, i.e.,  8  x 3 = 24, followed by a blank, and then 8 x 7 = 56. We conclude from here that the pattern as:

1st, 3rd, 5th, 7th, 9th, 11th, and 13th multiple of 8, where each multiple differs by 2. So, our pattern for the blank column is as follows:

1. Third blank

8 x 5 = 40

2. Fifth blank

8  x 9 = 72

3. Sixth blank

8  x 11 = 88

4. Seventh blank

8  x 13 = 104

So, the pattern formed is: 8, 24, 40, 56, 72, 88, 104.

In this game, you are again asked to fill in the missing places:

___, ___, 80, 72, 64, ___

In this pattern,  the decreasing order 8 times table can be seen in which the last term will be 8 x 7 = 56, while the remaining terms are as follows:

1st blank = 8 x 12 = 96, and 2nd blank = 8 x 11 = 88

So, the pattern formed is 96, 88, 8, 72, 64, 56

Let’s take another example: If you are asked to find the 5th multiple of 8 from the given following options, how will you determine it?

1. 24

2. 34

3. 56

4. 40

We will start with the options. If we look at 24, it is the third multiple of 8, i.e., 8 x 3 = 24.

The second option isn’t a multiple of 8, then 56 is the 7th multiple of 8. Lastly, 40 is the 5th multiple of 8, it’s because 8 x 5 = 40. So, option 4 is the correct answer.

List of Multiples of 8

Multiples of 8 can be infinite. Here is the list of the first 20 multiples of 8.

Multiples of 8

 Multiplication of 8 With  An Integer Multiples 0f 8 8 x  1 = 8 8 x  2 = 16 8 x  3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x10= 80 8 x 11= 88 8 x 12= 96 8 x 13= 104 8 x 14= 112 8 x 15= 120 8 x 16= 128 8 x 17 = 136 8 x 18= 144 8 x 19= 152 8 x 20= 160

### Multiples of 8 by Division

As we know that multiplication and division operations are inverse of each other, multiple of any number can be found even by the division operation.

Suppose we have to check whether 120 is multiple of 8 or not.

120 8 = 15 Since 120 is completely divisible by 8 we can say that 120 is a multiple of 8.

### What is Common Multiple?

Common multiples are defined as the common multiple number from the set of two or more numbers. Let us understand from the given example.

For example 3 and 9:

Some of Multiples of 3 are 3, 6, 9,12, 15, 18, 21, 24, 27,30, 33, 36, 39

Some of Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81,90, 99, 108, 117

Common of 3 and 9 are Multiples 9, 18, 27, 36

### Solved Examples

Writ Down The 5 Multiples of The Following

1. 6

Solution: 6, 18, 36, 48, 54.

1. 13

Solution: 13, 36, 39, 52, 65.

### Quiz Time

Write down any three multiples of the following numbers

1. 15

2. 20

3. 17

4. 23

### Fun Facts

• A Number has an infinite number of multiples.

• Every number is a multiple of itself.

• Every multiple of a given number is greater than or equal to that given number.

• Zero is a multiple of every number.

• First multiple of any given number is the number itself.

1. How to Find LCM of Two Numbers?

LCM  stands for the least common multiple. The least common multiple is the smallest number that is the common multiple of all the given numbers. To find the LCM of given numbers first we have to write all the factors of the given numbers. Now multiply each factor the maximum number of times it occurs in both the numbers. You will get the LCM of the numbers.

For example: Let us find the LCM of 30 and 50

First, calculate the prime factors

30 = 2 x 3 x 5

50 = 2 x 5 x 5

Now, LCM = 2 x 5 x 3 x 5

= 150

2. What are the Factors of a Number?

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6.