124 LearnersLast updated on May 26th, 2025
Multiples of 30
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 30.
What are the Multiples of 30?
Now, let us learn more about multiples of 30. Multiples of 30 are the numbers you get when you multiply 30 by any whole number, including zero. Each number has an infinite number of multiples, including a multiple of itself. In multiplication, a multiple of 30 can be denoted as 30 × 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 30 × 1 will give us 30 as the product. Multiples of 30 will be larger or equal to 30.
List of First 20 Multiples of 30
Multiples of 30 include the products of 30 and an integer. Multiples of 30 are divisible by 30 evenly. The first few multiples of 30 are given below:
| TABLE OF 30 (1-10) | |
|---|---|
|
30 x 1 = 30 |
30 x 6 = 180 |
|
30 x 2 = 60 |
30 x 7 = 210 |
|
30 x 3 = 90 |
30 x 8 = 240 |
|
30 x 4 = 120 |
30 x 9 = 270 |
|
30 x 5 = 150 |
30 x 10 = 300 |
| TABLE OF 30 (11-20) | |
|---|---|
|
30 x 11 = 330 |
30 x 16 = 480 |
|
30 x 12 = 360 |
30 x 17 = 510 |
|
30 x 13 = 390 |
30 x 18 = 540 |
|
30 x 14 = 420 |
30 x 19 = 570 |
|
30 x 15 = 450 |
30 x 20 = 600 |
Now, we know the first few multiples of 30. They are 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300,...
Operations with Multiples of 30
Understanding the multiples of 30 helps solve mathematical problems and boosts our multiplication and division skills. When working with multiples of 30, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of first 5 Multiples of 30:
30, 60, 90, 120, and 150 are the first five multiples of 30. When multiplying 30 from 1 to 5, we get these numbers as the products. So, the sum of these multiples is:
30 + 60 + 90 + 120 + 150 = 450
When we add the first 5 multiples of 30, the answer will be 450.
Subtraction of first 5 Multiples of 30:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 30, 60, 90, 120, and 150 are the first five multiples of 30. So, let us calculate it as given below:
30 - 60 = -30
-30 - 90 = -120
-120 - 120 = -240
-240 - 150 = -390
Hence, the result of subtracting the first 5 multiples of 30 is -390.
Average of first 5 Multiples of 30:
To calculate the average, we need to identify the sum of the first 5 multiples of 30, 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 30 is 450.
30 + 60 + 90 + 120 + 150 = 450
Next, divide the sum by 5:
450 ÷ 5 = 90
90 is the average of the first 5 multiples of 30.
Product of First 5 Multiples of 30:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 30 include: 30, 60, 90, 120, and 150. Now, the product of these numbers is:
30 × 60 × 90 × 120 × 150 = 29,160,000,000
The product of the first 5 multiples of 30 is 29,160,000,000.
Division of First 5 Multiples of 30:
While we perform division, we get to know how many times 30 can fit into each of the given multiples. 30, 60, 90, 120, and 150 are the first 5 multiples of 30.
30 ÷ 30 = 1
60 ÷ 30 = 2
90 ÷ 30 = 3
120 ÷ 30 = 4
150 ÷ 30 = 5
The results of dividing the first 5 multiples of 30 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 30
While working with multiples of 30, 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 30. 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 30 refer to the products we get while multiplying 30 with other numbers. For example, multiples of 30 include 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300…
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. When 30 is divided by any of these numbers, the remainder will be zero. These are the factors of 30, meaning that these numbers can divide 30 without any remainder.
Factors of 30:
30 ÷ 1 = 30
30 ÷ 2 = 15
30 ÷ 3 = 10
30 ÷ 5 = 6
30 ÷ 6 = 5
30 ÷ 10 = 3
30 ÷ 15 = 2
30 ÷ 30 = 1
Multiples of 30 Examples
Problem 1
Sophia is organizing a charity event where each ticket costs $30. If she sells tickets every week and sells 30 tickets each week, how much money will she have collected after 5 weeks?
$4,500
Explanation
Each week, she sells 30 tickets. To find the total amount collected after 5 weeks, we multiply the number of tickets by the price per ticket and then by the number of weeks.
Tickets sold each week = 30
Price per ticket = $30
Number of weeks = 5
30 × 30 × 5 = $4,500
Therefore, Sophia will have collected $4,500 after 5 weeks.
Problem 2
At a car dealership, every batch of cars delivered contains 30 vehicles. If the first three batches have been delivered, how many cars have been received in total?
90 cars
Explanation
Each batch contains 30 cars. To find the total number of cars received after three batches, we identify the first three multiples of 30.
30 × 1 = 30
30 × 2 = 60
30 × 3 = 90
Therefore, a total of 90 cars have been received.
Problem 3
A bakery produces boxes of cookies in batches of 30. If they have 30 boxes on each shelf and there are 4 shelves, how many boxes of cookies are there in total in the bakery?
120 boxes
Explanation
To find the total number of boxes, we need to count the shelves and multiply by the number of boxes on each shelf.
Number of shelves = 4
Number of boxes on each shelf = 30
4 × 30 = 120
Therefore, there are 120 boxes of cookies in total.
Problem 4
Emma is collecting stamps. She organizes them in albums, with each album holding 5 pages, and each page holding 30 stamps. How many stamps does she have in total if all albums are full?
150 stamps
Explanation
To find the total number of stamps, we multiply the number of pages by the number of stamps on each page, and then by the number of albums if each album is similar.
Number of pages per album = 5
Number of stamps per page = 30
5 × 30 = 150
Therefore, Emma has a total of 150 stamps.
Problem 5
Daniel is setting up chairs for a conference. He has 30 chairs in the first row, 60 in the second, and 90 in the third. How many chairs are there in total?
180 chairs
Explanation
The first row has 30 chairs, the second row has 60, and the third row has 90. To find the total, we add the chairs from each row.
30 + 60 + 90 = 180
Therefore, there are a total of 180 chairs set up for the conference.
FAQs on Multiples of 30
1.How do you find the multiples of 30?
2.What is the LCM of 5 and 30?
3.What are the real-life applications of Multiples of 30?
4.Are multiples of 30 finite or infinite?
5.Is there any odd multiples of 30?
Important Glossaries for Multiples of 30
- Multiple: A multiple represents the product of a number that is multiplied by an integer. For example, multiples of 30 include 30, 60, 90, 120, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 30 are the numbers that consist of the number pattern of 30.
- 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 30 are even numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 2, 3, 5, 6, 10, 15, and 30 are the divisors of 30.
- LCM (Least Common Multiple): The smallest multiple that is exactly divisible by each number of a set. For example, the LCM of 5 and 30 is 30.
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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
