169 LearnersLast updated on May 26th, 2025
Multiples of 840
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 840.
What are the Multiples of 840?
Now, let us learn more about multiples of 840. Multiples of 840 are the numbers you get when you multiply 840 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 840 can be denoted as 840 × 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 840 × 1 will give us 840 as the product. Multiples of 840 will be larger or equal to 840.
List of First 20 Multiples of 840
Multiples of 840 include the products of 840 and an integer. Multiples of 840 are divisible by 840 evenly. The first few multiples of 840 are given below:
| TABLE OF 840 (1-10) | |
|---|---|
|
840 x 1 = 840 |
840 x 6 = 5040 |
|
840 x 2 = 1680 |
840 x 7 = 5880 |
|
840 x 3 = 2520 |
840 x 8 = 6720 |
|
840 x 4 = 3360 |
840 x 9 = 7560 |
|
840 x 5 = 4200 |
840 x 10 = 8400 |
| TABLE OF 840 (11-20) | |
|---|---|
|
840 x 11 = 9240 |
840 x 16 = 13440 |
|
840 x 12 = 10080 |
840 x 17 = 14280 |
|
840 x 13 = 10920 |
840 x 18 = 15120 |
|
840 x 14 = 11760 |
840 x 19 = 15960 |
|
840 x 15 = 12600 |
840 x 20 = 16800 |
Now, we know the first few multiples of 840. They are 0, 840, 1680, 2520, 3360, 4200, 5040, 5880, 6720, 7560, 8400,...
Operations with Multiples of 840
Understanding the multiples of 840 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 840, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of First 5 Multiples of 840
840, 1680, 2520, 3360, and 4200 are the first five multiples of 840. When multiplying 840 from 1 to 5, we get these numbers as the products.
So, the sum of these multiples is:
840 + 1680 + 2520 + 3360 + 4200 = 12600
When we add the first 5 multiples of 840, the answer will be 12600.
Subtraction of First 5 Multiples of 840
When we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 840, 1680, 2520, 3360, and 4200 are the first five multiples of 840. So, let us calculate it as given below:
840 - 1680 = -840
-840 - 2520 = -3360
-3360 - 3360 = -6720
-6720 - 4200 = -10920
Hence, the result of subtracting the first 5 multiples of 840 is -10920.
Average of First 5 Multiples of 840
To calculate the average, we need to identify the sum of the first 5 multiples of 840, and then divide it by the count, i.e., 5. Because there are 5 multiples presented in the calculation. Averaging helps us understand the concepts of central tendencies and other values. We know the sum of the first 5 multiples of 840 is 12600.
840 + 1680 + 2520 + 3360 + 4200 = 12600
Next, divide the sum by 5:
12600 ÷ 5 = 2520
2520 is the average of the first 5 multiples of 840.
Product of First 5 Multiples of 840
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 840 include: 840, 1680, 2520, 3360, and 4200. Now, the product of these numbers is:
840 × 1680 × 2520 × 3360 × 4200 = 10,485,760,000,000,000
The product of the first 5 multiples of 840 is 10,485,760,000,000,000.
Division of First 5 Multiples of 840
While we perform division, we get to know how many times 840 can fit into each of the given multiples. 840, 1680, 2520, 3360, and 4200 are the first 5 multiples of 840.
840 ÷ 840 = 1
1680 ÷ 840 = 2
2520 ÷ 840 = 3
3360 ÷ 840 = 4
4200 ÷ 840 = 5
The results of dividing the first 5 multiples of 840 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 840
While working with multiples of 840, 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 840. 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 840 refer to the products we get while multiplying 840 with other numbers. For example, multiples of 840 include 0, 840, 1680, 2520, 3360, 4200, 5040, 5880, 6720, 7560, 8400, …
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. When 840 is divided by any of these factors, the remainder will be zero.
Multiples of 840 Examples
Problem 1
At a community event, volunteers are preparing gift bags for attendees. Each volunteer can prepare 840 gift bags in a day. If there are 5 volunteers working each day, how many gift bags will be prepared in total after 3 days?
12,600 gift bags
Explanation
Each volunteer prepares 840 gift bags per day. With 5 volunteers working for 3 days, we calculate the total number of gift bags:
Gift bags per volunteer per day = 840
Number of volunteers = 5
Number of days = 3
Total gift bags = 840 × 5 × 3 = 12,600
Therefore, 12,600 gift bags will be prepared in total.
Problem 2
A factory produces batches of 840 units of a product every hour. If they operate for 7 hours a day, how many units are produced in a week (assuming they work 5 days a week)?
29,400 units
Explanation
The factory produces 840 units per hour. To find the weekly production:
Units per hour = 840
Operating hours per day = 7
Days in a week = 5
Total units produced = 840 × 7 × 5 = 29,400
Therefore, the factory produces 29,400 units in a week.
Problem 3
A gardener is planting trees along a long pathway. She plants a tree every 840 meters. If the pathway is 6 kilometers long, how many trees will she plant?
7 trees
Explanation
First, convert kilometers to meters: 6 km = 6,000 meters.
Distance between trees = 840 meters
Pathway length = 6,000 meters
Number of trees = 6,000 ÷ 840 ≈ 7.14
Since she can only plant whole trees, she will plant 7 trees along the pathway.
Problem 4
A music festival distributes tickets in bulk orders of 840 tickets. If a sponsor orders 9 such bulk orders, how many tickets does the sponsor receive?
7,560 tickets
Explanation
Each bulk order contains 840 tickets. For 9 bulk orders:
Tickets per bulk order = 840
Number of bulk orders = 9
Total tickets = 840 × 9 = 7,560
Therefore, the sponsor receives 7,560 tickets.
Problem 5
In a warehouse, packages are stored in stacks of 840 each. If there are 14 stacks, how many packages are there in total?
11,760 packages
Explanation
Each stack contains 840 packages. For 14 stacks:
Packages per stack = 840
Number of stacks = 14
Total packages = 840 × 14 = 11,760
Therefore, there are 11,760 packages in total in the warehouse.
FAQs on Multiples of 840
1.How do you find the multiples of 840?
2.What is the LCM of 7 and 840?
3.What are the real-life applications of Multiples of 840?
4.Are multiples of 840 finite or infinite?
5.Is there any odd multiple of 840?
6.How can poems help children in United States memorize the Multiplication Table and Multiples of 840?
7.Can learning the Multiplication Table influence creativity in solving Multiples of 840 challenges for kids in United States?
8.How do language and cultural differences in United States affect the way children learn the Multiplication Table and Multiples of 840?
9.What role does brain development play in mastering the Multiplication Table and Multiples of 840 among early learners in United States?
Important Glossaries for Multiples of 840
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 840 include 840, 1680, 2520, 3360, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 840 are the numbers that consist of the number pattern of 840.
- 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 840 are even numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840 are the divisors of 840.
- LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers. For example, the LCM of 7 and 840 is 840.
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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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