Multiples are the numbers 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 x (- 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:
Now, for the ten’s digit in each column in Row 1 will be written from 0 to 4 as:
Similarly, we will write for the ten’s digit from 4 to 8 in Row 2 as:
So, we get the first 10 multiples of 8 as:
08
16
24
32
40
48
56
64
72
80
Similarly, 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 17 = 136
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:
Now, write the numbers from 0 to 8 in the following manner:
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 inverses of each other, multiple of any number can be found even by the division operation.
Suppose we have to check whether 120 is a 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 numbers 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
Write Down The 5 Multiples of The Following
1. 6
Solution: 6, 18, 36, 48, 54.
2. 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
Each 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.
The first multiple of any given number is the number itself.
Relevance of studying Multiples in Maths
Multiples have a significant role to play in Maths and in our lives. It forms the very basis of all mathematical calculations. Something as simple as going to the salon every 5th day of the week will require the knowledge of multiples. Businessmen use multiples to quantify a businesses’ growth and opportunities. They also use multiples to compare how other rival companies are faring. Multiples need to be grasped at the basic level while in school so that all students are able to calculate well and get their foundations strong. Learning how to perform simple calculations now will assist them in understanding the complex ones later on.