183 LearnersLast updated on May 26th, 2025
Multiples of 105
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 105.
What are the Multiples of 105?
Now, let us learn more about multiples of 105. Multiples of 105 are the numbers you get when you multiply 105 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 105 can be denoted as 105 × 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 105 × 1 will give us 105 as the product. Multiples of 105 will be larger or equal to 105.
List of First 20 Multiples of 105
Multiples of 105 include the products of 105 and an integer. Multiples of 105 are divisible by 105 evenly. The first few multiples of 105 are given below:
Now, we know the first few multiples of 105. They are 0, 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050,...
| TABLE OF 105 (1-10) | |
|---|---|
|
105 x 1 = 105 |
105 x 6 = 630 |
|
105 x 2 = 210 |
105 x 7 = 735 |
|
105 x 3 = 315 |
105 x 8 = 840 |
|
105 x 4 = 420 |
105 x 9 = 945 |
|
105 x 5 = 525 |
105 x 10 = 1050 |
| TABLE OF 105 (11-20) | |
|---|---|
|
105 x 11 = 1155 |
105 x 16 = 1680 |
|
105 x 12 = 1260 |
105 x 17 = 1785 |
|
105 x 13 = 1365 |
105 x 18 = 1890 |
|
105 x 14 = 1470 |
105 x 19 = 1995 |
|
105 x 15 = 1575 |
105 x 20 = 2100 |
Operations with Multiples of 105
Understanding the multiples of 105 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 105, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of First 5 Multiples of 105:
105, 210, 315, 420, and 525 are the first five multiples of 105. When multiplying 105 from 1 to 5, we get these numbers as the products. So, the sum of these multiples is:
105 + 210 + 315 + 420 + 525 = 1575
When we add the first 5 multiples of 105, the answer will be 1575.
Subtraction of First 5 Multiples of 105:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 105, 210, 315, 420, and 525 are the first five multiples of 105. So, let us calculate it as given below:
105 - 210 = -105
-105 - 315 = -420
-420 - 420 = -840
-840 - 525 = -1365
Hence, the result of subtracting the first 5 multiples of 105 is -1365.
Average of First 5 Multiples of 105:
To calculate the average, we need to identify the sum of the first 5 multiples of 105, and then divide it by the count, i.e., 5. Because there are 5 multiples presented in the calculation. We know the sum of the first 5 multiples of 105 is 1575.
105 + 210 + 315 + 420 + 525 = 1575
Next, divide the sum by 5:
1575 ÷ 5 = 315
315 is the average of the first 5 multiples of 105.
Product of First 5 Multiples of 105:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 105 include: 105, 210, 315, 420, and 525. Now, the product of these numbers is:
105 × 210 × 315 × 420 × 525 = 1,948,091,250,000
The product of the first 5 multiples of 105 is 1,948,091,250,000.
Division of First 5 Multiples of 105:
While we perform division, we get to know how many times 105 can fit into each of the given multiples. 105, 210, 315, 420, and 525 are the first 5 multiples of 105.
105 ÷ 105 = 1
210 ÷ 105 = 2
315 ÷ 105 = 3
420 ÷ 105 = 4
525 ÷ 105 = 5
The results of dividing the first 5 multiples of 105 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 105
While working with multiples of 105, 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 105. 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 105 refer to the products we get while multiplying 105 with other numbers. For example, multiples of 105 include 0, 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050,…
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105. When 105 is divided by these numbers, the remainder will be zero. These are the factors of 105, meaning that these numbers can divide 105 without any remainder.
Factors of 105:
105 ÷ 1 = 105
105 ÷ 3 = 35
105 ÷ 5 = 21
105 ÷ 7 = 15
105 ÷ 15 = 7
105 ÷ 21 = 5
105 ÷ 35 = 3
105 ÷ 105 = 1
Multiples of 105 Examples
Problem 1
In a factory, every machine produces 105 widgets per hour. If the factory operates 5 machines simultaneously for 6 hours a day, how many widgets are produced in a day?
3,150 widgets
Explanation
Each machine produces 105 widgets per hour. With 5 machines operating for 6 hours, we multiply to find the total production.
Widgets per machine per hour = 105
Number of machines = 5
Operating hours per day = 6
105 × 5 × 6 = 3,150
The factory produces 3,150 widgets in a day.
Problem 2
During a fundraising event, a group of volunteers decides to bake cookies in batches of 105. If three volunteers bake the first three multiples of 105 batches, how many batches does each volunteer bake?
The first three multiples of 105 are 105, 210, and 315. The volunteers bake 105, 210, and 315 batches respectively.
Explanation
We identify the first three multiples of 105:
105 × 1 = 105
105 × 2 = 210
105 × 3 = 315
Hence, each volunteer bakes 105, 210, and 315 batches, respectively.
Problem 3
A school organizes a marathon with checkpoints every 105 meters. If there are 7 checkpoints along the route, what is the total distance of the marathon?
735 meters
Explanation
Each checkpoint is placed 105 meters apart. With 7 checkpoints, we multiply to find the total distance.
Distance between checkpoints = 105 meters
Number of checkpoints = 7
105 × 7 = 735
Therefore, the marathon covers a total distance of 735 meters.
Problem 4
A farmer plants trees along a fence line in groups of 105. If he plans to have 4 such groups, how many trees does he need to plant in total?
420 trees
Explanation
The farmer plants trees in groups of 105. With 4 groups planned, we multiply to find the total number of trees.
Trees per group = 105
Number of groups = 4
105 × 4 = 420
So, the farmer needs to plant 420 trees in total.
Problem 5
In a library, books are arranged in stacks containing 105 books each. If there are stacks of 105, 210, and 315 books respectively, how many books are there altogether?
630 books
Explanation
The stacks contain 105, 210, and 315 books. We add these to find the total number of books.
105 + 210 + 315 = 630
Therefore, a total of 630 books are there in the library.
FAQs on Multiples of 105
1.How do you find the multiples of 105?
2. What is the LCM of 7 and 105?
3.What are the real-life applications of multiples of 105?
4.Are multiples of 105 finite or infinite?
5.Is there any odd multiple of 105?
Important Glossaries for Multiples of 105
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 105 include 105, 210, 315, 420, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 105 are the numbers that consist of the number pattern of 105.
- Odd number: An odd number refers to any number that cannot be divided by 2 without leaving a remainder. The last digits of odd numbers are 1, 3, 5, 7, or 9. Some multiples of 105 are odd numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 3, 5, 7, 15, 21, 35, and 105 are the divisors of 105.
- LCM (Least Common Multiple): The smallest multiple that is a common multiple of two or more numbers. For example, the LCM of 7 and 105 is 105.
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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
