169 LearnersLast updated on May 26th, 2025
Multiples of 315
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 315.
What are the Multiples of 315?
Now, let us learn more about multiples of 315. Multiples of 315 are the numbers you get when you multiply 315 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 315 can be denoted as 315 × 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 315 × 1 will give us 315 as the product. Multiples of 315 will be larger or equal to 315.
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List of First 20 Multiples of 315
Multiples of 315 include the products of 315 and an integer. Multiples of 315 are divisible by 315 evenly. The first few multiples of 315 are given below:
| TABLE OF 315 (1-10) | |
|---|---|
|
315 x 1 = 315 |
315 x 6 = 1890 |
|
315 x 2 = 630 |
315 x 7 = 2205 |
|
315 x 3 = 945 |
315 x 8 = 2520 |
|
315 x 4 = 1260 |
315 x 9 = 2835 |
|
315 x 5 = 1575 |
315 x 10 = 3150 |
| TABLE OF 315 (11-20) | |
|---|---|
|
315 x 11 = 3465 |
315 x 16 = 5040 |
|
315 x 12 = 3780 |
315 x 17 = 5355 |
|
315 x 13 = 4095 |
315 x 18 = 5670 |
|
315 x 14 = 4410 |
315 x 19 = 5985 |
|
315 x 15 = 4725 |
315 x 20 = 6300 |
Now, we know the first few multiples of 315. They are 0, 315, 630, 945, 1260, 1575, 1890, 2205, 2520, 2835, 3150,...
Operations with Multiples of 315
Understanding the multiples of 315 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 315, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of First 5 Multiples of 315:
315, 630, 945, 1260, and 1575 are the first five multiples of 315. When multiplying 315 from 1 to 5, we get these numbers as the products.
So, the sum of these multiples is:
315 + 630 + 945 + 1260 + 1575 = 4725
When we add the first 5 multiples of 315, the answer will be 4725.
Subtraction of First 5 Multiples of 315:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 315, 630, 945, 1260, and 1575 are the first five multiples of 315. So, let us calculate it as given below:
315 - 630 = -315
-315 - 945 = -1260
-1260 - 1260 = -2520
-2520 - 1575 = -4095
Hence, the result of subtracting the first 5 multiples of 315 is -4095.
Average of First 5 Multiples of 315:
To calculate the average, we need to identify the sum of the first 5 multiples of 315, 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 315 is 4725.
315 + 630 + 945 + 1260 + 1575 = 4725
Next, divide the sum by 5:
4725 ÷ 5 = 945
945 is the average of the first 5 multiples of 315.
Product of First 5 Multiples of 315:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 315 include: 315, 630, 945, 1260, and 1575. Now, the product of these numbers is:
315 × 630 × 945 × 1260 × 1575 = 148,913,347,025,000
The product of the first 5 multiples of 315 is 148,913,347,025,000.
Division of First 5 Multiples of 315:
While we perform division, we get to know how many times 315 can fit into each of the given multiples. 315, 630, 945, 1260, and 1575 are the first 5 multiples of 315.
315 ÷ 315 = 1
630 ÷ 315 = 2
945 ÷ 315 = 3
1260 ÷ 315 = 4
1575 ÷ 315 = 5
The results of dividing the first 5 multiples of 315 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 315
While working with multiples of 315, 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 315. 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 315 refer to the products we get while multiplying 315 with other numbers. For example, multiples of 315 include 0, 315, 630, 945, 1260, 1575, 1890, 2205, 2520, 2835, 3150, ...
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. When 315 is divided by these numbers, the remainder will be zero.
Factors of 315:
315 ÷ 1 = 315
315 ÷ 3 = 105
315 ÷ 5 = 63
315 ÷ 7 = 45
315 ÷ 9 = 35
315 ÷ 15 = 21
Mistake 2
Skipping Multiples while Listing
Be careful when listing each multiple in the sequence. Otherwise, it may lead to incorrect calculations and results. Children sometimes skip multiples when writing them. To clearly understand the issue, take a look at this:
Multiples of 315 include 315, 630, 945, 1260, 1575, 1890, ..., 3150, 3465, ...
If children do this, they may get confused and mix up the sequential order. So, maintain a consistent order by including each multiple.
Mistake 3
Forgetting to Check the Results with Multiplication
If you are adding or subtracting multiples of 315, the result will still be a multiple of 315. For example, children may write, 315 + 630 = 950 (which is wrong and the correct answer is 945)
This is incorrect because 950 is not a multiple of 315. The same applies to subtraction. When you are adding or subtracting, ensure that the results are multiples of 315.
Mistake 4
Ignoring the Concept of Zero
Don’t forget that zero is a multiple of every number. The very first multiple of 315, and any other number, is zero, and it has a valid value. Remember this:
315 × 0 = 0
Mistake 5
Using Addition Instead of Multiplication
Apply multiplication for calculations and check the results for accuracy. Sometimes, children may incorrectly add 315 + 315 + 315 + 315 + 315. Instead of adding too many values, use multiplication. Calculate 315 × n for the nth multiple.
For example, instead of 315 + 315 + 315 + 315 + 315, calculate it as given below:
315 × 5 = 1575
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Multiples of 315 Examples
Problem 1
A local art gallery hosts monthly exhibitions, and each exhibition features 315 paintings. If the gallery organizes exhibitions every month for 6 months, how many paintings are displayed in total during this period?
1890 paintings
Explanation
Each month, the gallery features 315 paintings. To find the total number of paintings displayed over 6 months, we multiply the number of paintings per exhibition by the number of months.
Paintings per exhibition = 315
Number of months = 6
315 × 6 = 1890
Therefore, a total of 1890 paintings are displayed in 6 months.
Problem 2
A music festival schedules performances in multiples of 315 minutes throughout the day. The first performance lasts 315 minutes, the second lasts 630 minutes, and the third lasts 945 minutes. How many minutes of performances are there in total for these three performances?
1890 minutes
Explanation
The durations of the performances are the first three multiples of 315.
315 × 1 = 315
315 × 2 = 630
315 × 3 = 945
Total performance time = 315 + 630 + 945 = 1890
Thus, there are 1890 minutes of performances in total.
Problem 3
A factory produces 315 widgets every hour. If the factory operates for 8 hours in a day, how many widgets does it produce in a day?
2520 widgets
Explanation
To find the total daily production, multiply the number of widgets produced per hour by the number of hours in operation.
Widgets per hour = 315
Number of hours = 8
315 × 8 = 2520
Therefore, the factory produces 2520 widgets in a day.
Problem 4
A farmer plants 315 seeds in each row of his field. If he plants 7 rows, how many seeds does he plant in total?
2205 seeds
Explanation
To find the total number of seeds planted, multiply the number of seeds per row by the number of rows.
Seeds per row = 315
Number of rows = 7
315 × 7 = 2205
Hence, the farmer plants a total of 2205 seeds.
Problem 5
A company packages its products in boxes containing 315 items each. If they ship out 5 such boxes, how many items are shipped in total?
1575 items
Explanation
To determine the total number of items shipped, multiply the number of items per box by the number of boxes.
Items per box = 315
Number of boxes = 5
315 × 5 = 1575
Therefore, 1575 items are shipped in total.
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FAQs on Multiples of 315
1.How do you find the multiples of 315?
2.What is the LCM of 21 and 315?
3.What are the real-life applications of Multiples of 315?
4.Are multiples of 315 finite or infinite?
5.Are there any odd multiples of 315?
6.How can poems help children in United States memorize the Multiplication Table and Multiples of 315?
7.Can learning the Multiplication Table influence creativity in solving Multiples of 315 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 315?
9.What role does brain development play in mastering the Multiplication Table and Multiples of 315 among early learners in United States?
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Important Glossaries for Multiples of 315
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 315 include 315, 630, 945, 1260, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 315 are the numbers that consist of the number pattern of 315.
- Odd number: An odd number is any number that is not divisible by 2. The last digits of odd numbers are 1, 3, 5, 7, or 9. Some multiples of 315 are odd.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315 are the divisors of 315.
- Least Common Multiple (LCM): The smallest multiple that is exactly divisible by each of the numbers. For example, the LCM of 21 and 315 is 315.
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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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