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156 LearnersLast updated on February 3rd, 2025
Multiples of 84
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 84.
What are the Multiples of 84?
Now, let us learn more about multiples of 84. Multiples of 84 are the numbers you get when you multiply 84 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 84 can be denoted as 84 × 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 84 × 1 will give us 84 as the product. Multiples of 84 will be larger or equal to 84.
List of First 20 Multiples of 84
Multiples of 84 include the products of 84 and an integer. Multiples of 84 are divisible by 84 evenly. The first few multiples of 84 are given below:
| TABLE OF 84 (1-10) | |
|---|---|
|
84 x 1 = 84 |
84 x 6 = 504 |
|
84 x 2 = 168 |
84 x 7 = 588 |
|
84 x 3 = 252 |
84 x 8 = 672 |
|
84 x 4 = 336 |
84 x 9 = 756 |
|
84 x 5 = 420 |
84 x 10 = 840 |
| TABLE OF 84 (11-20) | |
|---|---|
|
84 x 11 = 924 |
84 x 16 = 1344 |
|
84 x 12 = 1008 |
84 x 17 = 1428 |
|
84 x 13 = 1092 |
84 x 18 = 1512 |
|
84 x 14 = 1176 |
84 x 19 = 1596 |
|
84 x 15 = 1260 |
84 x 20 = 1680 |
Now, we know the first few multiples of 84. They are 0, 84, 168, 252, 336, 420, 504, 588, 672, 756, 840,.
Operations with Multiples of 84
Understanding the multiples of 84 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 84, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of First 5 Multiples of 84:
84, 168, 252, 336, and 420 are the first five multiples of 84. When multiplying 84 from 1 to 5, we get these numbers as the products.
So, the sum of these multiples is:
84 + 168 + 252 + 336 + 420 = 1260
When we add the first 5 multiples of 84, the answer will be 1260.
Subtraction of First 5 Multiples of 84:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 84, 168, 252, 336, and 420 are the first five multiples of 84. So, let us calculate it as given below:
84 - 168 = -84
-84 - 252 = -336
-336 - 336 = -672
-672 - 420 = -1092
Hence, the result of subtracting the first 5 multiples of 84 is -1092.
Average of First 5 Multiples of 84:
To calculate the average, we need to identify the sum of the first 5 multiples of 84 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 84 is 1260.
84 + 168 + 252 + 336 + 420 = 1260
Next, divide the sum by 5:
1260 ÷ 5 = 252
252 is the average of the first 5 multiples of 84.
Product of First 5 Multiples of 84:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 84 include: 84, 168, 252, 336, and 420. Now, the product of these numbers is:
84 × 168 × 252 × 336 × 420 = 1,590,797,568,000
The product of the first 5 multiples of 84 is 1,590,797,568,000.
Division of First 5 Multiples of 84:
While we perform division, we get to know how many times 84 can fit into each of the given multiples. 84, 168, 252, 336, and 420 are the first 5 multiples of 84.
84 ÷ 84 = 1
168 ÷ 84 = 2
252 ÷ 84 = 3
336 ÷ 84 = 4
420 ÷ 84 = 5
The results of dividing the first 5 multiples of 84 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 84
While working with multiples of 84, 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 84. 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 84 refer to the products we get while multiplying 84 with other numbers. For example, multiples of 84 include 0, 84, 168, 252, 336, 420, 504, 588, 672, 756, 840….
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. When 84 is divided by these numbers, the remainder will be zero. These are the factors of 84 meaning that these numbers can divide 84 without any remainder.
Multiples of 84 Examples
Problem 1
In a community garden, there are 84 tomato plants in each section. The garden expands, adding 3 more sections each year, each with 84 tomato plants. How many tomato plants will there be in total at the end of 3 years?
1,008 tomato plants
Explanation
Each year, 3 sections are added, each containing 84 tomato plants. To find the total number of tomato plants at the end of 3 years, multiply the number of sections added by 84 and then by the number of years.
Additional sections per year = 3
Number of plants per section = 84
Number of years = 3
3 × 84 × 3 = 756
Total plants after 3 years = initial section + additional plants = 84 + 756 = 840
Therefore, there will be 1,008 tomato plants in total.
Problem 2
A concert hall has seating arranged in rows, with each row having 84 seats. If the first three rows are filled to capacity, how many people are seated in these rows?
252 people
Explanation
The first three rows are full, and each row contains 84 seats. To find the total number of people seated, multiply the number of rows by the number of seats per row.
Number of rows = 3
Seats per row = 84
3 × 84 = 252
Therefore, 252 people are seated in the first three rows.
Problem 3
A factory produces 84 widgets every hour. If the factory operates for 12 hours a day, how many widgets does it produce in a day?
1,008 widgets
Explanation
To find the total production in a day, multiply the number of widgets produced per hour by the number of operating hours.
Widgets per hour = 84
Operating hours = 12
84 × 12 = 1,008
Therefore, the factory produces 1,008 widgets in a day.
Problem 4
A library has 84 reference books on each shelf. If there are 5 shelves dedicated to reference books, how many reference books are there in total?
420 reference books
Explanation
To find the total number of reference books, multiply the number of books on each shelf by the number of shelves.
Books per shelf = 84
Number of shelves = 5
84 × 5 = 420
Therefore, there are 420 reference books in total.
Problem 5
During a charity event, every volunteer packs 84 food parcels. If there are 7 volunteers, how many food parcels are packed in total?
588 food parcels
Explanation
To find the total number of food parcels packed, multiply the number of parcels each volunteer packs by the number of volunteers.
Parcels per volunteer = 84
Number of volunteers = 7
84 × 7 = 588
Therefore, 588 food parcels are packed in total.
FAQs on Multiples of 84
1.How do you find the multiples of 84?
2.What is the LCM of 7 and 84?
3.What are the real-life applications of multiples of 84?
4.Are multiples of 84 finite or infinite?
5.Is there any odd multiple of 84?
Important Glossaries for Multiples of 84
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 84 include 84, 168, 252, 336, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 84 are the numbers that consist of the number pattern of 84.
- 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 84 are even numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84 are the divisors of 84.
- LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers. For example, the LCM of 7 and 84 is 84.
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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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