How to Find Multiples of 17 Step by Step with 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 with Examples and Explanation
1. What are the multiples of 17?
The multiples of 17 are numbers obtained by multiplying 17 with natural numbers (1, 2, 3, and so on). For example, the first five multiples of 17 are 17, 34, 51, 68, and 85. These multiples follow the pattern 17 × n, where n is a whole number.
2. How do you find multiples of 17?
To find the multiples of 17, multiply 17 by any natural number. You can also use repeated addition, adding 17 repeatedly. For example, the first three multiples are 17 × 1 = 17, 17 × 2 = 34, and 17 × 3 = 51. This process helps in listing multiples step-by-step for easy understanding and practice.
3. What are the first five multiples of 17?
The first five multiples of 17 are 17, 34, 51, 68, and 85. They are calculated by multiplying 17 by numbers 1 to 5 respectively: 17×1=17, 17×2=34, 17×3=51, 17×4=68, and 17×5=85.
4. What is the difference between multiples and factors of 17?
The multiples of 17 are numbers obtained by multiplying 17 with any whole number, giving infinite values like 17, 34, 51, etc. Factors of 17 are numbers that divide 17 exactly without leaving a remainder. Since 17 is a prime number, its factors are only 1 and 17. Understanding this difference helps clear common exam confusions.
5. What is the table of 17?
The table of 17 lists the products of 17 multiplied by numbers starting from 1 up to 20 or more. For example, 17×1=17, 17×2=34, ..., 17×20=340. This tabular format aids quick reference and revision for exams.
6. What are the common multiples of 17 and 7?
Common multiples of 17 and 7 are numbers that are multiples of both 17 and 7. To find them, list multiples of each and identify the shared numbers. The smallest common multiple (LCM) of 17 and 7 is 119 because 17×7=119. Recognizing common multiples helps in solving problems related to LCM and fractions.
7. Why is 34 a multiple of 17 but not a factor?
34 is a multiple of 17 because 17×2=34, meaning it is formed by multiplying 17 by a whole number. However, it is not a factor of 17 because it does not divide 17 exactly without leaving a remainder. Factors must divide the original number perfectly, while multiples are the product of the original number and an integer.
8. Why do students confuse multiples and factors of 17 in exam problems?
Students often confuse multiples and factors because both involve multiplication and division concepts. Factors divide the number exactly, whereas multiples are results of multiplication. For 17, a prime number, factors are limited to 1 and 17, but multiples are infinite. Clear examples and practice help resolve this confusion effectively.
9. Can multiples of 17 be negative numbers?
Yes, multiples of 17 can be negative if you allow multiplication by negative integers. For example, -17, -34, and -51 are all multiples of 17 because they equal 17 multiplied by -1, -2, and -3 respectively. However, typically, multiples are considered as positive numbers in exam contexts unless specified.
10. How can multiples of 17 help with LCM questions in board exams?
Multiples of 17 are essential for finding the Least Common Multiple (LCM) when combined with multiples of other numbers. By listing multiples of 17 and another number, students can identify the smallest number that appears in both lists, which is the LCM. This skill is frequently tested in board exams and aids in solving fraction and ratio problems.
11. Why is it important to practice tables and multiples for maths competitions?
Practicing tables and multiples builds speed and accuracy in arithmetic operations, which are crucial in competitive exams. It enhances mental math skills, helps recognize patterns quickly, and improves problem-solving efficiency. Mastery of multiples of numbers like 17 supports tackling higher-level questions with confidence.
12. Can a number be both a multiple and a factor of 17?
A number can be both a multiple and a factor of 17 only if it equals 17 itself. Since 17 is a prime number, its factors are only 1 and 17, while multiples include 17 and larger products like 34, 51, etc. Therefore, 17 is the only number that is both a multiple and a factor of 17.
