List Of Multiples Of 17 Formula And Solved Examples
The concept of multiples of 17 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Understanding these multiples can improve number sense and calculation skills, especially for school maths and competitive exams.
Understanding Multiples of 17
A multiple of 17 refers to any number you get when you multiply 17 by a whole number (natural number). These numbers are important in multiplication, number patterns, and for finding least common multiples (LCM) in maths. Some examples include 34, 51, and 68. This idea helps in arithmetic progressions, times tables, and divisibility problems.
Formula Used in Multiples of 17
The standard formula is: \( 17 \times n \), where \( n \) is any whole number (1, 2, 3, ...).
Here’s a helpful table to understand multiples of 17 more clearly:
Multiples of 17 Table (First 20)
| n | Multiplication | Multiple of 17 |
|---|---|---|
| 1 | 17 × 1 | 17 |
| 2 | 17 × 2 | 34 |
| 3 | 17 × 3 | 51 |
| 4 | 17 × 4 | 68 |
| 5 | 17 × 5 | 85 |
| 6 | 17 × 6 | 102 |
| 7 | 17 × 7 | 119 |
| 8 | 17 × 8 | 136 |
| 9 | 17 × 9 | 153 |
| 10 | 17 × 10 | 170 |
| 11 | 17 × 11 | 187 |
| 12 | 17 × 12 | 204 |
| 13 | 17 × 13 | 221 |
| 14 | 17 × 14 | 238 |
| 15 | 17 × 15 | 255 |
| 16 | 17 × 16 | 272 |
| 17 | 17 × 17 | 289 |
| 18 | 17 × 18 | 306 |
| 19 | 17 × 19 | 323 |
| 20 | 17 × 20 | 340 |
This table shows the regular multiplication pattern for multiples of 17, which is also called the table of 17 and is handy for exams and mental maths.
Worked Example – Solving Multiples of 17 Problems
Let’s find if 119 is a multiple of 17.
2. \( 119 \div 17 = 7 \) exactly, with no remainder.
3. Since 17 × 7 = 119, 119 is a multiple of 17.
Now, let’s list all multiples of 17 between 35 and 100.
2. The multiples that fall between 35 and 100 are 51, 68, and 85.
Common Multiples and Even/Odd Multiples
Common multiples of 17 and 7 are numbers that are multiples of both. To find them, look for numbers divisible by both. The first common multiple is the LCM (17 × 7 = 119), next is 238, 357, and so on.
Odd multiples of 17 up to 100 are: 17, 51, 85. Even multiples up to 100 are: 34 and 68.
Multiples vs Factors of 17
A multiple of 17 is found by multiplying 17 by any integer (like 34, 51, 68, etc). A factor of 17 is a number that divides 17 exactly. Since 17 is prime, it has only two factors: 1 and 17. Review factors of 17 if you’re confused by the difference.
Practice Problems
- Write the first five multiples of 17.
- Is 255 a multiple of 17?
- List all multiples of 17 between 68 and 150.
- Which of the following is not a multiple of 17: 34, 51, 77?
Common Mistakes to Avoid
- Confusing multiples of 17 with factors of 17.
- Forgetting to use the correct multiplication sequence when building the list.
- Stopping the sequence early or skipping numbers due to miscalculation.
Real-World Applications
The concept of multiples of 17 appears in group arrangements (like packaging 17 items per box), timetables, and scheduling tasks that repeat every 17 days. Mastering this helps in maths competitions, mental arithmetic, and quantitative exams. Vedantu helps students see how maths concepts like these appear in day-to-day life.
Quick Revision & Tips
- Makes exam calculation faster when you know the table of 17 by memory.
- Compare with multiples of 18 and multiples of 15 to recognize patterns.
- Use multiples for fast LCM and division calculations in exams.
We explored the idea of multiples of 17, how to apply it, solve related problems, and understand its real-life relevance. Practice more with Vedantu to build confidence in these maths concepts.
Related Concepts and Further Reading
FAQs on Multiples Of 17 Explained With Patterns And Examples
1. What are the multiples of 17?
The multiples of 17 are numbers obtained by multiplying 17 by whole numbers. In general, they are written as 17 × n, where n is a whole number.
- First few multiples: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170
- Formula: Multiples of 17 = 17n
- They continue infinitely because n can be any whole number.
2. How do you find the multiples of 17?
To find the multiples of 17, multiply 17 by whole numbers like 1, 2, 3, and so on.
- Step 1: Start with 17 × 1 = 17
- Step 2: 17 × 2 = 34
- Step 3: 17 × 3 = 51
- Continue multiplying by the next whole number.
3. What is the formula for multiples of 17?
The formula for the multiples of 17 is 17n, where n is a whole number (0, 1, 2, 3, ...).
- If n = 1, 17n = 17
- If n = 5, 17n = 85
- If n = 10, 17n = 170
4. What are the first 10 multiples of 17?
The first 10 multiples of 17 are 17 multiplied by numbers from 1 to 10.
- 17 × 1 = 17
- 17 × 2 = 34
- 17 × 3 = 51
- 17 × 4 = 68
- 17 × 5 = 85
- 17 × 6 = 102
- 17 × 7 = 119
- 17 × 8 = 136
- 17 × 9 = 153
- 17 × 10 = 170
5. Is 51 a multiple of 17?
Yes, 51 is a multiple of 17 because 17 divides 51 exactly.
- 51 ÷ 17 = 3
- Since the result is a whole number, 51 is divisible by 17.
6. How many multiples of 17 are there?
There are infinitely many multiples of 17 because you can multiply 17 by any whole number.
- 17 × 1 = 17
- 17 × 100 = 1700
- 17 × 1000 = 17000
7. What is the smallest multiple of 17?
The smallest multiple of 17 is 0 if whole numbers include zero, and 17 if considering positive multiples only.
- 17 × 0 = 0
- 17 × 1 = 17
8. What is the difference between factors and multiples of 17?
The factors of 17 divide 17 exactly, while the multiples of 17 are numbers obtained by multiplying 17.
- Factors of 17: 1 and 17 (since 17 is prime)
- Multiples of 17: 17, 34, 51, 68, ...
9. How can you check if a number is a multiple of 17?
A number is a multiple of 17 if it is divisible by 17 without leaving a remainder.
- Step 1: Divide the number by 17.
- Step 2: If the remainder is 0, it is a multiple.
- Example: 136 ÷ 17 = 8, so 136 is a multiple of 17.
10. Are multiples of 17 always odd?
No, multiples of 17 can be odd or even depending on the multiplier.
- 17 × 1 = 17 (odd)
- 17 × 2 = 34 (even)
- 17 × 3 = 51 (odd)
