What are the Multiples of 23?
When the number 23 is multiplied by any natural number, the result is known as a multiple of 23. Every multiple of 23 can be written as 23n where n can be any natural number. We have to multiply 23 with the first n natural numbers to obtain the first n multiples of 23.
For example, if we multiply 23 by 4, the product is 92. As a result, we define 92 as a multiple of 23. Another concept to remember here is that the product of two numbers is a multiple of both numbers. Hence, 92 is a multiple of 4 as well.
Hence, the multiples of 23 will be:
23, 46, 69, 92, 115, 138,…
Thus, from the above observations, we can say that the multiple of 23 can be obtained by multiplying natural numbers by 23.
For example 115, 138 and 161 are all multiples of 23 because we can get these numbers by multiplying 23 with specific natural numbers.
Also, we can observe that the difference between each succeeding number and the preceding number is 23, that is,
46 – 23 = 23,
69 – 46 = 23,
92 – 69 = 23 and so on.
Finding the Multiples of 23 by Repeated Addition
Repeated addition means adding a number to itself repeatedly. We can use repeated addition to find the multiples of a number.
If we want to find the first ten multiples of 23, we can write it in the following way:
23 x 1 = 23 | 23 | |
|---|---|---|
23 x 2 = 46 | 23 + 23 | Here 23 is added two times |
23 x 3 = 69 | 23 + 23 + 23 | Here 23 is added three times |
23 x 4 = 92 | 23 + 23 + 23 + 23 | Here 23 is added four times |
23 x 5 = 115 | 23 + 23 + 23 + 23 + 23 | Here 23 is added five times |
23 x 6 = 138 | 23 + 23 + 23 + 23 + 23 + 23 | Here 23 is added six times |
23 x 7 = 161 | 23 + 23 + 23 + 23 + 23 + 23 + 23 | Here 23 is added seven times |
23 x 8 = 184 | 23 + 23 + 23 + 23 + 23 + 23 + 23 + 23 | Here 23 is added eight times |
23 x 9 = 207 | 23 + 23 + 23 + 23 + 23 + 23 + 23 + 23 + 23 | Here 23 is added nine times |
23 x 10 = 230 | 23 + 23 + 23 + 23 + 23 + 23 + 23 + 23 + 23 + 23 | Here 23 is added ten times |
The ‘nth’ Multiple of 23
The n\(^{th}\) multiple of 23 can be obtained by either multiplying 23 by n or by adding 23 n times;
n\(^{th}\) multiple of 23 = 23 x n, or
n\(^{th}\) multiple of 23 = 23 + 23 + … n times
[Note: n is any natural number.]
Rapid Recall
The first ten multiples of 23 can be written as:
Solved Multiples of 23 Examples
Example 1: Is 125 a multiple of 23?
Solution:
List the multiples of 23.
23, 46, 69, 92, 115, 138, …
So, 125 is not a multiple of 23.
Example 2: What is the 7th multiple of 23?
Solution:
The 7th multiple of 23 can be obtained by the repeated addition of 23 7 times:
23 + 23 + 23 + 23 + 23 + 23 + 23
= 161
Hence, the 7th multiple of 23 is 161.
Example 3: Four friends, John, Tom, Ray and Annie decided to buy pens. Tom has 23 more pens than John, Ray has 23 more pens than Tom and Annie has 23 more pens than Ray. If John buys 23 pens, make a list of pens Tom, Ray and Annie have.
Solution:
If we observe the pattern mentioned in the question, we see the repeated addition of 23.
23 + 23 + 23 + 23
They are simply the first four multiples of 23.
The multiples of 23 are 23, 46, 69, 92, 115, 138, …
So, John bought 23 pens.
Tom bought 46 pens.
Ray bought 69 pens and
Annie bought 92 pens.
Hence, John, Tom, Ray and Annie bought 23, 46, 69 and 92 pens, respectively.
The multiples of a number are obtained by multiplying the number with a natural number.
The smallest multiple of 23 is 23 itself.
A number can be multiplied indefinitely, so it can have an infinite number of multiples.
The factor of a number is an integer that can divide the number evenly. However, the multiple of a number is obtained when the number is multiplied by any natural number.