What are the Multiples of 11?
When the number 11 is multiplied by any natural number, the result is known as a multiple of 11.
For example: If we multiply 11 by 5, the product will be 55. So, we say that 55 is a multiple of 11.
The multiples of 11 can be expressed in the form of 11n, where n is a natural number.
And, n = 1, 2, 3, 4, 5, 6, …
The multiples of 11 will be:
11, 22, 33, 44, 55, 66, …
Thus, from the above observations, we can say that the multiple of 11 can be obtained by multiplying natural numbers by 11.
For example, 110, 121, and 132 are all multiples of 11 because we can get all these numbers by multiplying 11 by a natural number.
\( 11~\times~10~=~110\) | 11 multiplied by 10 to get 110 |
| \( 11~\times~11~=~121\) | 11 multiplied by 11 to get 121 |
| \( 11~\times~12~=~132\) | 11 multiplied by 12 to get 132 |
Also, we can observe that the difference between two successive multiples is 11, that is,
22 – 11 = 11,
33 – 22 = 11,
44 – 33 = 11, and so on.
How to find Multiples by Repeated Addition?
Repeated addition means adding a number to itself, repeatedly. Repeated addition can also be used to determine the multiples of any number.
We can find the multiples using repeated addition in the following way:
11 × 1 = 11 | 11 | |
11 × 2 = 22 | Or 11 + 11 = 22 | Here 11 added twice |
11 × 3 = 33 | Or 11 + 11 + 11 = 33 | Here 11 added thrice |
11 × 4 = 44 | Or 11 + 11 + 11 + 11 = 44 | Here 11 added four times |
11 × 5 = 55 | Or 11 + 11 + 11 + 11 + 11 = 55 | Here 11 added five times |
11 × 6 = 66 | Or 11 + 11 + 11 + 11 + 11 + 11 = 66 | Here 11 added six times |
The nth Multiple of 11
The nth multiple of 11 can be obtained by either multiplying 11 by n or by adding 11, n times:
nth multiple of 11 = 11 x n, or
nth multiple of 11 = 11 + 11 + ……… n times
[Note: n is any natural number.]
List of the First Ten Multiples of 11
The first ten multiples of 11 are the products of 11 and the first ten natural numbers.
11 × 1 | 11 |
11 × 2 | 22 |
11 × 3 | 33 |
11 × 4 | 44 |
11 × 5 | 55 |
11 × 6 | 66 |
11 × 7 | 77 |
11 × 8 | 88 |
11 × 9 | 99 |
11 × 10 | 110 |
Multiples and Factors of 11
A factor of 11 is a natural number which when multiplied with another number results in 11. Hence the number 11 is a multiple of its factors.
For example, we know that 1 and 11 are factors of 11. So 11 is a multiple of 1 and 11.
Similarly, 22 is a multiple of 11. So 11 is a factor of 22.
[Note: To check whether a number is a multiple of 11 or not, divide the number by 11 and observe the remainder value. If the remainder is zero the number is a multiple of 11 otherwise not.]
Rapid Recall
Solved Multiples of 11 Examples
Example 1: Johnny needs 33 batteries for a science project. Batteries are sold in packs of 10 and packs of 11. Which pack should Johnny buy so he has no leftover batteries?
Solution:
Use the division method to determine whether 33 is a multiple of 10 or not.
33 \( \div\) 10 = 3 R3
So, 10 is not a factor of 33 and 33 is not a multiple of 10.
Similarly , use the division method to determine whether 33 is a multiple of 11 or not.
33 \( \div\) 11 = 3 R0
So, 11 is a factor of 33 and 33 is a multiple of 11.
Hence, Johnny should buy packs of 11 batteries.
Example 2: Is 110 a multiple of 11?
Solution:
List the multiples of 11.
11, 22, 33, 44, 55, 66, 77, 88, 99, 110, …
So, 110 is a multiple of 11.
Example 3: How can the division method be used to show that 50 is not a multiple of 11?
Solution:
To determine using the division method:
Dividing 50 by 11, we get,
50 ÷ 11 = 4 R6
Hence, 50 is not a multiple of the number 11.
A multiple is defined as a number which we get by multiplying a particular number by another number.
The first 10 multiples of 11 are:
11, 22, 33, 44, 55, 66,…..
So, the 4th multiple of 11 is 44.
The multiples of the number 11 are the numbers that we get when 11 is multiplied by any natural number. The multiples of 11 can be expressed in the form of 11n, where n is a natural number.
A number can have an infinite number of multiples.
The factor of a number is an integer which can evenly divide the number, whereas, the multiple of a number is obtained when the number is multiplied with any natural number.