What are multiples?
When a natural number is multiplied by another natural number, the product is known as a multiple of both the numbers multiplied.
For example: If we multiply 6 by 5, then the product is 30. As a result, we define 30 as a multiple of 6 and 5.
To check if a number is a multiple of the given number can use the following methods.
- Listing multiples
Natural numbers are numbers such as 1, 2, 3, 4, 5, 6, … Therefore, to find the multiples of 6, for instance, we can multiply each natural number by 6. Hence, the multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
2. Finding the factors
To check if 81 is a factor of 9, we check if 9 is a factor of 81. So, we divide 81 by 9,\(\frac{81}{9}=9\) R0.
On division, the remainder is 0. Hence, 9 is a factor of 81 and thus 81 is a multiple of 9.
We can also use divisibility rules to check if 9 is a factor of 81 or not. 8+1=9, the sum of the digits of 81 is a multiple of 9. Hence 9 is a factor of 81, therefore 81 is a multiple of 9.
Finding Multiples by Repeated Addition
Repeated addition implies that a number is added to itself in a repeated manner. We can also use repeated addition to find the multiples of a number.
For example: We can find the first three multiples of 5 using repeated addition.
51 | 5 | |
52 | 5+5 | Here 5 is added two times |
53 | 5+5+5 | Here 5 is added three times |
Solved Examples
Example 1: What is the 14th multiple of 7?
Solution:
The 14th multiple of 7 can be obtained by the repeated addition of 7 for 14 times;
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 98
Hence, the 14th multiple of 7 is 98.
Example 2: Sam wants to give chocolate bars to the children playing in the park. Sam distributed 8 packets consisting of 13 white chocolate bars each and 8 packets of 11 dark chocolate bars each. What is the total number of chocolate bars that Sam distributed?
Solution:
Sam gives 8 packets of 13 white chocolate bars each.
Therefore, the number of white chocolate bars = 813 =104
Sam also gives 8 packets of 11 dark chocolate bars each.
Hence, the number of dark chocolate bars = 811 = 88
Total number of chocolate bars distributed = 104 + 88 = 192
Hence, Same distributed 192 chocolate bars in total.
Example 3: Check whether 38 is a multiple of 5.
Let’s list the multiples of 5 to check if 38 is a multiple of 5 or not.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40 …
In the above list, 38 is not included.
Hence, 38 is not a multiple of 5.
Example 4: Verify if 19 is a multiple of 2.
To check if 19 is a multiple of 2, let’s first check if 2 is a factor of 19. So we divide 19 by 2.
\(\frac{19}{2}=9 R1\)
On division, we get a remainder as 1.
Hence, 2 is not a factor of 19. Therefore, 19 is not a multiple of 2.
A number can be multiplied by infinite natural numbers, so it can have an infinite number of multiples.
If a number is multiplied with another number then the resultant product is known as a multiple, and the numbers being multiplied are known as the factors of the resultant product.
The smallest multiple of a number is the number itself obtained by multiplying it with 1.