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115 LearnersLast updated on February 11th, 2025
Multiples of 214
In math, multiples are the products we get when 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 214.
What are the Multiples of 214?
Now, let us learn more about multiples of 214. Multiples of 214 are the numbers you get when you multiply 214 by any whole number, including zero. Each number has an infinite number of multiples, including a multiple of itself.
In multiplication, a multiple of 214 can be denoted as 214 × 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 214 × 1 will give us 214 as the product. Multiples of 214 will be larger or equal to 214.
List of First 20 Multiples of 214
Multiples of 214 include the products of 214 and an integer. Multiples of 214 are divisible by 214 evenly. The first few multiples of 214 are given below:
| TABLE OF 214 (1-10) | |
|---|---|
|
214 x 1 = 214 |
214 x 6 = 1284 |
|
214 x 2 = 428 |
214 x 7 = 1498 |
|
214 x 3 = 642 |
214 x 8 = 1712 |
|
214 x 4 = 856 |
214 x 9 = 1926 |
|
214 x 5 = 1070 |
214 x 10 = 2140 |
| TABLE OF 214 (11-20) | |
|---|---|
|
214 x 11 = 2354 |
214 x 16 = 3424 |
|
214 x 12 = 2568 |
214 x 17 = 3638 |
|
214 x 13 = 2782 |
214 x 18 = 3852 |
|
214 x 14 = 2996 |
214 x 19 = 4066 |
|
214 x 15 = 3210 |
214 x 20 = 4280 |
Now, we know the first few multiples of 214. They are 0, 214, 428, 642, 856, 1070, 1284, 1498, 1712, 1926, 2140, ...
Operations with Multiples of 214
Understanding the multiples of 214 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 214, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of first 5 Multiples of 214:
214, 428, 642, 856, and 1070 are the first five multiples of 214. When multiplying 214 from 1 to 5, we get these numbers as the products.
So, the sum of these multiples is:
214 + 428 + 642 + 856 + 1070 = 3210
When we add the first 5 multiples of 214, the answer will be 3210.
Subtraction of first 5 Multiples of 214:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 214, 428, 642, 856, and 1070 are the first five multiples of 214. So, let us calculate it as given below:
214 - 428 = -214
-214 - 642 = -856
-856 - 856 = -1712
-1712 - 1070 = -2782
Hence, the result of subtracting the first 5 multiples of 214 is -2782.
Average of first 5 Multiples of 214:
To calculate the average, we need to identify the sum of the first 5 multiples of 214, 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 214 is 3210.
214 + 428 + 642 + 856 + 1070 = 3210
Next, divide the sum by 5:
3210 ÷ 5 = 642
642 is the average of the first 5 multiples of 214.
Product of First 5 Multiples of 214:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 214 include: 214, 428, 642, 856, and 1070. Now, the product of these numbers is:
214 × 428 × 642 × 856 × 1070 = 6,448,853,670,080
The product of the first 5 multiples of 214 is 6,448,853,670,080.
Division of First 5 Multiples of 214:
While we perform division, we get to know how many times 214 can fit into each of the given multiples. 214, 428, 642, 856, and 1070 are the first 5 multiples of 214.
214 ÷ 214 = 1
428 ÷ 214 = 2
642 ÷ 214 = 3
856 ÷ 214 = 4
1070 ÷ 214 = 5
The results of dividing the first 5 multiples of 214 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 214
While working with multiples of 214, 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 214. 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 214 refer to the products we get while multiplying 214 with other numbers. For example, multiples of 214 include 0, 214, 428, 642, 856, 1070, 1284, 1498, 1712, 1926, 2140,….
Multiples of 214 Examples
Problem 1
An art gallery organizes exhibitions every 214 days. If the gallery continues this pattern, how many exhibitions will be held after 642 days?
3 exhibitions
Explanation
To find the number of exhibitions, divide the total number of days by the interval of days between exhibitions.
Days per exhibition = 214
Total days = 642
642 ÷ 214 = 3
Therefore, 3 exhibitions will be held after 642 days.
Problem 2
A farmer is planting trees in his orchard. He plants trees in rows with each row containing 214 trees. If he has planted 856 trees, how many rows of trees has he planted?
4 rows
Explanation
To find the number of rows, divide the total number of trees by the number of trees per row.
Trees per row = 214
Total trees = 856
856 ÷ 214 = 4
Therefore, the farmer has planted 4 rows of trees.
Problem 3
A company is distributing promotional items in batches of 214. If they distribute 1070 items, how many complete batches were distributed?
5 batches
Explanation
To determine the number of complete batches, divide the total number of items by the number of items per batch.
Items per batch = 214
Total items = 1070
1070 ÷ 214 = 5
Therefore, 5 complete batches were distributed.
Problem 4
In a library, each shelf can hold 214 books. If the library has a total of 1284 books, how many fully filled shelves are there?
6 shelves
Explanation
To find the number of fully filled shelves, divide the total number of books by the capacity of each shelf.
Books per shelf = 214
Total books = 1284
1284 ÷ 214 = 6
Therefore, there are 6 fully filled shelves.
Problem 5
A marathon event is held every 214 days in a city. If this pattern continues, how many events will have been held in a span of 1926 days?
9 events
Explanation
To calculate the number of events, divide the total number of days by the interval between each marathon event.
Days per event = 214
Total days = 1926
1926 ÷ 214 = 9
Therefore, 9 marathon events will be held in 1926 days.
FAQs on Multiples of 214
1.How do you find the multiples of 214?
2.What is the LCM of 7 and 214?
3.What are the real-life applications of Multiples of 214?
4.Are multiples of 214 finite or infinite?
5.Is there any odd multiple of 214?
Important Glossaries for Multiples of 214
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 214 include 214, 428, 642, 856, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 214 are the numbers that consist of the number pattern of 214.
- 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 214 are even numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. Numbers like 1, 2, 107, and 214 are the divisors of 214.
- Product: The result of multiplying two or more numbers. For instance, 214 × 3 = 642, making 642 a product of 214 and 3.
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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.
Fun Fact
: She has songs for each table which helps her to remember the tables
