How to Quickly Find Multiples of 3 (Step-by-Step Guide & Examples)
The concept of multiples of 3 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Whether you're skip-counting, solving puzzles, or checking for divisibility, knowing the set of numbers that are multiples of 3 helps sharpen your basic Arithmetic skills and lays a strong foundation for advanced maths.
What Is Multiples of 3?
A multiple of 3 is any number that can be written as 3 times an integer (like 3, 6, 9, 12, etc.). You’ll find this concept applied in areas such as number patterns, divisibility tests, and solving word problems involving sets or groups. Multiples of 3 are commonly asked in MCQs, fill-in-the-blanks, Olympiad practice, and other maths exams.
Key Formula for Multiples of 3
Here’s the standard formula: \( \text{Multiple of 3} = 3n \), where \( n \) is any whole number (0, 1, 2, 3, ...).
Cross-Disciplinary Usage
Multiples of 3 are not only useful in Maths but also play an important role in Computer Science (like coding number patterns), Physics (measuring units in threes), Music beats, and daily logical reasoning. Students preparing for JEE, NTSE, or Olympiad will notice multiples of 3 featured in many questions around LCM, HCF, and divisibility.
Step-by-Step Illustration
- List the first 10 multiples of 3 using the formula:
3 × 1 = 33 × 2 = 63 × 3 = 93 × 4 = 123 × 5 = 153 × 6 = 183 × 7 = 213 × 8 = 243 × 9 = 273 × 10 = 30So, the first 10 multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 3 up to 100 (Table)
| n | Multiple of 3 | n | Multiple of 3 | n | Multiple of 3 |
|---|---|---|---|---|---|
| 1 | 3 | 12 | 36 | 23 | 69 |
| 2 | 6 | 13 | 39 | 24 | 72 |
| 3 | 9 | 14 | 42 | 25 | 75 |
| 4 | 12 | 15 | 45 | 26 | 78 |
| 5 | 15 | 16 | 48 | 27 | 81 |
| 6 | 18 | 17 | 51 | 28 | 84 |
| 7 | 21 | 18 | 54 | 29 | 87 |
| 8 | 24 | 19 | 57 | 30 | 90 |
| 9 | 27 | 20 | 60 | 31 | 93 |
| 10 | 30 | 21 | 63 | 32 | 96 |
| 11 | 33 | 22 | 66 | 33 | 99 |
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for checking if a number is a multiple of 3: Add up the digits of the number. If their sum is a multiple of 3, then so is the number! Many students use this trick during timed exams to save crucial seconds.
Example Trick: Check if 123 is a multiple of 3:
- Add the digits: 1 + 2 + 3 = 6
- 6 is a multiple of 3, so 123 is a multiple of 3.
Tricks like this are practical in competitive exams like NTSE, Olympiads, and even JEE. Vedantu’s live sessions include many more shortcuts for maths problem-solving.
Try These Yourself
- Write the first five multiples of 3.
- Check if 48 is a multiple of 3.
- Find all multiples of 3 between 30 and 60.
- Identify the non-multiple of 3 from the list: 12, 15, 19.
Frequent Errors and Misunderstandings
- Assuming multiples of 3 are the same as factors of 3.
- Forgetting that 0 is also a multiple of 3 (3 × 0 = 0).
- Skipping steps when multiplying, leading to missed numbers in the list.
Relation to Other Concepts
The idea of multiples of 3 connects closely with topics such as factors of 3 and LCM and HCF. Mastering this helps in understanding divisibility rules and is useful when learning multiples of 6 and multiples of 9 as well.
Classroom Tip
A quick way to remember multiples of 3 is to skip count: 3, 6, 9, 12, 15... Vedantu’s teachers often use catchy skip-counting songs and colorful number charts during live classes to help you visualize the pattern and recall the sequence quickly.
We explored multiples of 3—from their definition, formula, visual tables, to common mistakes and connections to broader maths. Keep practicing with Vedantu’s worksheets or online mock tests, and you’ll find yourself answering questions about multiples of 3 with confidence!
FAQs on Multiples of 3: Meaning, List & Solved Problems
1. What are multiples of 3?
Multiples of 3 are numbers that result from multiplying 3 by any integer. These numbers are always divisible by 3 without leaving a remainder. For example, 3, 6, 9, 12, 15, and so on, are all multiples of 3.
2. How do I find the multiples of 3?
To find multiples of 3, simply multiply 3 by consecutive integers (1, 2, 3, 4, and so on). Alternatively, you can use the divisibility rule: if the sum of a number's digits is divisible by 3, then the number itself is a multiple of 3.
3. Are all multiples of 3 odd numbers?
No. Multiples of 3 can be both odd and even numbers. For instance, 3, 9, and 15 are odd multiples, while 6, 12, and 18 are even multiples.
4. Is 0 a multiple of 3?
Yes, 0 is a multiple of 3 because 3 multiplied by 0 equals 0. In fact, 0 is a multiple of every integer.
5. What is the difference between factors and multiples?
Factors are numbers that divide evenly into a given number. Multiples are the results of multiplying a number by integers. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, while some multiples of 12 are 12, 24, 36, and 48.
6. How can I quickly check if a number is divisible by 3?
Add up the digits of the number. If the sum is divisible by 3, then the original number is also divisible by 3 (and therefore a multiple of 3). For example, consider the number 27: 2 + 7 = 9, and 9 is divisible by 3, so 27 is a multiple of 3.
7. List the first ten multiples of 3.
The first ten multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
8. What are the first five multiples of 30?
The first five multiples of 30 are: 30, 60, 90, 120, 150.
9. What are some real-world examples of multiples of 3?
Examples include arranging objects in groups of three (e.g., eggs in a carton), counting items in threes (e.g., steps in a staircase), or calculating the total cost of items priced at multiples of 3 (e.g., three pencils at ₹10 each).
10. How are multiples of 3 used in solving problems?
Understanding multiples of 3 is crucial for solving various mathematical problems, including those involving divisibility, patterns, and finding the least common multiple (LCM) of numbers. It aids in simplifying calculations and recognizing number relationships.
11. Is 48 a multiple of 3?
No. 4 + 8 = 12, and 12 is divisible by 3, so 48 is a multiple of 3.
12. What is the largest multiple of 3 less than 100?
The largest multiple of 3 less than 100 is 99 (3 x 33).
