How to Find and Use Multiples of 30 in Maths
The concept of Multiples of 30 is an important foundation in number theory and arithmetic. Knowing how to find and work with multiples makes topics like factors, LCM, divisibility, and solving real-life math problems much easier. This concept appears frequently in school assessments and in entrance exams such as JEE, Olympiads, and NTSE.
Understanding Multiples of 30
A multiple of 30 is any number that can be written as \( 30 \times n \), where \( n \) is a whole number (also called a natural number, starting from 1, 2, 3, ...). For example, the first few multiples of 30 are 30, 60, 90, 120, and 150. If you divide any multiple of 30 by 30, the answer will always be a whole number without any remainder.
List of Multiples of 30
Here are the first twenty multiples of 30, to help visualize the sequence:
| n | Multiple of 30 | Multiplication |
|---|---|---|
| 1 | 30 | 30 × 1 |
| 2 | 60 | 30 × 2 |
| 3 | 90 | 30 × 3 |
| 4 | 120 | 30 × 4 |
| 5 | 150 | 30 × 5 |
| 6 | 180 | 30 × 6 |
| 7 | 210 | 30 × 7 |
| 8 | 240 | 30 × 8 |
| 9 | 270 | 30 × 9 |
| 10 | 300 | 30 × 10 |
| 11 | 330 | 30 × 11 |
| 12 | 360 | 30 × 12 |
| 13 | 390 | 30 × 13 |
| 14 | 420 | 30 × 14 |
| 15 | 450 | 30 × 15 |
| 16 | 480 | 30 × 16 |
| 17 | 510 | 30 × 17 |
| 18 | 540 | 30 × 18 |
| 19 | 570 | 30 × 19 |
| 20 | 600 | 30 × 20 |
How to Find Multiples of 30
Finding a multiple of 30 is simple:
- Pick any whole number (let's call it n).
- Multiply 30 by n: \( 30 \times n \).
- The result is a multiple of 30.
Example: For \( n = 7 \), 30 × 7 = 210. So, 210 is a multiple of 30.
Properties and Patterns of Multiples of 30
- Every multiple of 30 is also a multiple of 2, 3, 5, 6, 10, and 15 (since all these numbers divide 30).
- All multiples of 30 are even numbers.
- The gap or difference between two consecutive multiples of 30 is always 30.
- If a number ends in 0 and the sum of its digits is a multiple of 3, it is a multiple of 30.
- Multiples of 30 have applications in scheduling, time, and grouping tasks.
- Multiples are infinite—you can keep multiplying 30 by larger numbers to get bigger multiples.
Multiples of 30 vs Factors of 30
| Multiples of 30 | Factors of 30 |
|---|---|
| Produced by multiplying 30 by any whole number (e.g., 30, 60, 90...) | Numbers that divide 30 exactly (e.g., 1, 2, 3, 5, 6, 10, 15, 30) |
| Infinite in number | Finite in number |
| Always greater than or equal to 30 | Always less than or equal to 30 |
Read more about Factors of 30.
Worked Examples
Example 1: Is 240 a multiple of 30?
- Divide 240 by 30: 240 ÷ 30 = 8
- Since the answer is a whole number, 240 is a multiple of 30.
Example 2: List all multiples of 30 between 55 and 150.
- First multiple of 30 after 55 is 60. Next: 90, 120, 150.
- Answer: 60, 90, 120, 150
Example 3: Find common multiples of 30 and 45 less than 200.
- Multiples of 30: 30, 60, 90, 120, 150, 180
- Multiples of 45: 45, 90, 135, 180
- Common multiples: 90, 180
Learn more about Common Multiples and LCM (Least Common Multiple).
Practice Problems
- List the first 7 multiples of 30.
- Is 330 a multiple of 30?
- Name two common multiples of 30 and 20.
- Fill in the blank: The 12th multiple of 30 is _____.
- True or False: All multiples of 30 are also multiples of 15?
- If you have 240 students and want to divide them into groups of 30, how many groups will you have?
- Find the sum of the first 5 multiples of 30.
Common Mistakes to Avoid
- Confusing multiples with factors. Remember, multiples are equal to or larger than the given number while factors are smaller or equal.
- Forgetting that multiples of 30 are always even.
- Trying to list factors when the question asks for multiples (and vice versa).
- Thinking the list of multiples is limited—it's actually infinite.
Real-World Applications
Multiples of 30 are used often in daily life. For example:
- Time: 60 minutes in an hour (which is a multiple of 30), and half-hour marks (e.g., 30, 60, 90 minutes) on a clock.
- Grouping: Organizing groups, packets, or teams with equal counts—for example, if one box has 30 chocolates, then 120 chocolates make 4 boxes (4 × 30 = 120).
- Finance: Payments or installments scheduled every 30 days (monthly).
- Problem-solving: Dividing items, scheduling events or using time tables, especially with multiples of 30.
At Vedantu, we simplify math topics like multiples and factors to help you master essential concepts and applications.
In this topic, we learned how to recognize, list, and use multiples of 30. Understanding multiples is important for number theory, divisibility, and many real-life applications. Mastering this topic helps you solve arithmetic, algebra, and grouping problems efficiently—and prepares you for school, entrance exams, and everyday problem-solving.
Continue exploring related concepts such as factors and multiples and arithmetic operations with Vedantu’s comprehensive lessons.
FAQs on Multiples of 30 Explained for Students
1. What are the first 10 multiples of 30?
The first ten multiples of 30 are numbers obtained by multiplying 30 by whole numbers 1 through 10. They are: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300. These are all even numbers and multiples of 6, 10, and 15.
2. What is the difference between multiples and factors?
Multiples of a number are obtained by multiplying that number by any whole number (e.g., multiples of 30 are 30, 60, 90...). Factors, on the other hand, are numbers that divide the given number exactly without leaving a remainder (e.g., factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30).
3. Is 240 a multiple of 30?
Yes, 240 is a multiple of 30 because 240 divided by 30 equals 8 (a whole number). This means 30 multiplied by 8 equals 240.
4. How do you find if a number is a multiple of 30?
To determine if a number is a multiple of 30, divide the number by 30. If the result is a whole number (no remainder), then the number is indeed a multiple of 30. For example, 90 ÷ 30 = 3, so 90 is a multiple of 30.
5. Are all multiples of 30 even numbers?
Yes, all multiples of 30 are even numbers. This is because 30 itself is an even number, and multiplying an even number by any whole number always results in an even number.
6. What are the first 5 multiples of 30?
The first five multiples of 30 are: 30, 60, 90, 120, and 150. These are found by multiplying 30 by 1, 2, 3, 4, and 5 respectively.
7. What is the sum of the first 10 multiples of 30?
The sum of the first ten multiples of 30 is 1650. This can be calculated using the formula for the sum of an arithmetic series or by simply adding the first ten multiples: 30 + 60 + 90 + ... + 300 = 1650.
8. What role do multiples of 30 play in time calculations (minutes, hours)?
Multiples of 30 are frequently used in time calculations because 30 minutes is half an hour. You'll see them used to mark half-hour intervals on clocks and in schedules. For example, 30 minutes, 60 minutes (1 hour), 90 minutes (1.5 hours), etc.
9. How are multiples and LCM (least common multiple) related?
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers. For example, to find the LCM of 30 and 45, you would find the smallest number that is a multiple of both. This involves finding the common multiples of both numbers and selecting the smallest.
10. Are all multiples of 30 also multiples of 15?
Yes, all multiples of 30 are also multiples of 15. This is because 30 is itself a multiple of 15 (30 = 15 x 2). Therefore, any number that is a multiple of 30 will always be divisible by 15.
11. What are the common multiples of 30 and 45?
Common multiples of 30 and 45 are numbers that are multiples of both 30 and 45. The first few common multiples are 90, 180, 270, 360, and so on. The least common multiple (LCM) of 30 and 45 is 90.
12. Is 6 a multiple of 30?
No, 6 is not a multiple of 30. A multiple of 30 is obtained by multiplying 30 by a whole number. Since there's no whole number that, when multiplied by 30, results in 6, 6 is not a multiple of 30. However, 30 is a multiple of 6.
13. Is 30 a multiple of 5?
Yes, 30 is a multiple of 5 because 30 can be obtained by multiplying 5 by a whole number (30 = 5 x 6).
