1275 LearnersLast updated on May 26th, 2025
Multiples of 198
In math, multiples are the products we get while multiplying a number with other numbers. Multiples play a key role in construction and design, counting groups of items, sharing resources equally, and managing time effectively. In this topic, we will learn the essential concepts of multiples of 198.
What are the Multiples of 198?
Now, let us learn more about multiples of 198. Multiples of 198 are the numbers you get when you multiply 198 by any whole number, along with zero. Each number has an infinite number of multiples, including a multiple of itself. In multiplication, a multiple of 198 can be denoted as 198 × n, where ‘n’ represents any whole number (0, 1, 2, 3,…). So, we can summarize that:
Multiple of a number = Number × Any whole number
For example, multiplying 198 × 1 will give us 198 as the product. Multiples of 198 will be larger or equal to 198.
List of First 20 Multiples of 198
Multiples of 198 include the products of 198 and an integer. Multiples of 198 are divisible by 198 evenly. The first few multiples of 198 are given below:
| TABLE OF 198 (1-10) | |
|---|---|
|
198 x 1 = 198 |
198 x 6 = 1188 |
|
198 x 2 = 396 |
198 x 7 = 1386 |
|
198 x 3 = 594 |
198 x 8 = 1584 |
|
198 x 4 = 792 |
198 x 9 = 1782 |
|
198 x 5 = 990 |
198 x 10 = 1980 |
| TABLE OF 198 (11-20) | |
|---|---|
|
198 x 11 = 2178 |
198 x 16 = 3168 |
|
198 x 12 = 2376 |
198 x 17 = 3366 |
|
198 x 13 = 2574 |
198 x 18 = 3564 |
|
198 x 14 = 2772 |
198 x 19 = 3762 |
|
198 x 15 = 2970 |
198 x 20 = 3960 |
Now, we know the first few multiples of 198. They are 0, 198, 396, 594, 792, 990, 1188, 1386, 1584, 1782, 1980,...
Operations with Multiples of 198
Understanding the multiples of 198 helps solve mathematical problems and boosts our multiplication and division skills. When working with multiples of 198, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of first 5 Multiples of 198:
198, 396, 594, 792, and 990 are the first five multiples of 198. When multiplying 198 from 1 to 5 we get these numbers as the products.
So, the sum of these multiples is:
198 + 396 + 594 + 792 + 990 = 2970
When we add the first 5 multiples of 198 the answer will be 2970.
Subtraction of first 5 Multiples of 198:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 198, 396, 594, 792, and 990 are the first five multiples of 198. So, let us calculate it as given below:
198 - 396 = -198
-198 - 594 = -792
-792 - 792 = -1584
-1584 - 990 = -2574
Hence, the result of subtracting the first 5 multiples of 198 is -2574.
Average of first 5 Multiples of 198:
To calculate the average, we need to identify the sum of the first 5 multiples of 198, and then divide it by the count, i.e., 5. Because there are 5 multiples presented in the calculation. Averaging helps us to understand the concepts of central tendencies and other values. We know the sum of the first 5 multiples of 198 is 2970.
198 + 396 + 594 + 792 + 990 = 2970
Next, divide the sum by 5:
2970 ÷ 5 = 594
594 is the average of the first 5 multiples of 198.
Product of First 5 Multiples of 198:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 198 include: 198, 396, 594, 792, and 990. Now, the product of these numbers is:
198 × 396 × 594 × 792 × 990 = 365,287,102,080
The product of the first 5 multiples of 198 is 365,287,102,080.
Division of First 5 Multiples of 198:
While we perform division, we get to know how many times 198 can fit into each of the given multiples. 198, 396, 594, 792, and 990 are the first 5 multiples of 198.
198 ÷ 198 = 1
396 ÷ 198 = 2
594 ÷ 198 = 3
792 ÷ 198 = 4
990 ÷ 198 = 5
The results of dividing the first 5 multiples of 198 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 198
While working with multiples of 198, we make common mistakes. Identifying these errors and understanding how to avoid them can be helpful. Below are some frequent mistakes and tips to avoid them:
Mistake 1
Confusing Multiples with Factors
Sometimes, students get confused between the multiples and factors of 198. A simple trick to differentiate between the two is to remember that multiples are the products of multiplication, while factors are the divisors of the number. Multiples of 198 refer to the products we get while multiplying 198 with other numbers. For example, multiples of 198 include 0, 198, 396, 594, 792, 990, 1188, 1386, 1584, 1782, 1980…
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198. When 198 is divided by these numbers, the remainder will be zero. These are the factors of 198 meaning that these numbers can divide 198 without any remainder.
Factors of 198:
198 ÷ 1 = 198
198 ÷ 2 = 99
198 ÷ 3 = 66
198 ÷ 6 = 33
Multiples of 198 Examples
Problem 1
n a factory, machines are producing widgets in batches. Each machine produces 198 widgets in a cycle, and there are 5 machines working simultaneously. If the machines complete 3 cycles in a day, how many widgets are produced in total at the end of the day?
2,970 widgets
Explanation
Each machine produces 198 widgets per cycle. To find the total number of widgets produced by all machines in a day, multiply the number of machines by the number of cycles and the number of widgets per cycle.
Number of machines = 5
Number of cycles = 3
Widgets per cycle = 198
(5 times 3 times 198 = 2,970)
Therefore, 2,970 widgets are produced at the end of the day.
Problem 2
A city council is planning to plant trees along a new highway. They plan to plant trees in groups that are multiples of 198. If they plant 198 trees in the first section, 396 in the second, and 594 in the third, how many trees have been planted in total?
1,188 trees
Explanation
The number of trees planted in each section is a multiple of 198. To find the total number of trees planted, add the trees from all sections.
First section: 198 trees
Second section: 396 trees
Third section: 594 trees
(198 + 396 + 594 = 1,188)
Therefore, a total of 1,188 trees have been planted.
Problem 3
In a library, books are organized in sets. Each set contains 198 books. If there are 7 sets of books, how many books does the library have in total?
1,386 books
Explanation
To find the total number of books, multiply the number of sets by the number of books per set.
Number of sets = 7
Books per set = 198
(7 times 198 = 1,386)
Therefore, the library has 1,386 books in total.
Problem 4
A marathon race is being organized, and the participants are grouped into waves. Each wave consists of 198 runners. If there are 4 waves, how many runners are participating in the marathon?
792 runners
Explanation
To determine the total number of participants, multiply the number of waves by the number of runners per wave.
Number of waves = 4
Runners per wave = 198
(4 times 198 = 792)
Therefore, there are 792 runners participating in the marathon.
Problem 5
A concert venue sells tickets in sections, with each section having seats that are a multiple of 198. If one section has 198 seats, another has 396 seats, and a third has 594 seats, how many seats are available in total?
1,188 seats
Explanation
The number of seats in each section is a multiple of 198. Add the number of seats in each section to find the total.
First section: 198 seats
Second section: 396 seats
Third section: 594 seats
(198 + 396 + 594 = 1,188)
Therefore, there are 1,188 seats available in total.
FAQs on Multiples of 198
1.How do you find the multiples of 198?
2.What is the LCM of 11 and 18?
3.What are the real-life applications of Multiples of 198?
4.Are multiples of 198 finite or infinite?
5.Is there any odd multiple of 198?
6.How can children in Australia use numbers in everyday life to understand Multiples of 198?
7.What are some fun ways kids in Australia can practice Multiples of 198 with numbers?
8.What role do numbers and Multiples of 198 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Multiples of 198 skills?
Important Glossaries for Multiples of 198
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 198 include 198, 396, 594, 792, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 198 are the numbers that consist of the number pattern of 198.
- Even number: An even number refers to any number that can be divisible by 2 without leaving any remainder. The last digits of even numbers are 0, 2, 4, 6, or 8. All multiples of 198 are even numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198 are the divisors of 198.
- Factor: A factor is a number that divides another number completely without leaving a remainder. The factors of 198 include 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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