What Are the First 20 Multiples of 14?
Understanding the Multiples of 14 is an essential building block in number theory and arithmetic. This concept is frequently tested in school math exams and forms the basis for advanced topics such as factors, divisibility, and finding common multiples – making it highly relevant for competitive exams and real-life problem-solving.
Understanding Multiples of 14
A multiple of 14 is any number that can be expressed as \( 14 \times n \), where \( n \) is a whole number (integer). This means 14, 28, 42, and 56 are all multiples of 14. Recognizing and working with multiples helps students manage division, fractions, and pattern problems more confidently. At Vedantu, we make these concepts simple and actionable for every learner.
How to Find Multiples of 14
To find a multiple of 14, multiply 14 by any whole number (including zero). For example, 14 × 4 = 56, so 56 is a multiple of 14. This process can start with 0 and continue infinitely:
- 14 × 0 = 0
- 14 × 1 = 14
- 14 × 2 = 28
- 14 × 3 = 42
- 14 × 4 = 56
- 14 × 5 = 70
- ...and so on.
The First 20 Multiples of 14
| n | Expression (14 × n) | Multiple |
|---|---|---|
| 1 | 14 × 1 | 14 |
| 2 | 14 × 2 | 28 |
| 3 | 14 × 3 | 42 |
| 4 | 14 × 4 | 56 |
| 5 | 14 × 5 | 70 |
| 6 | 14 × 6 | 84 |
| 7 | 14 × 7 | 98 |
| 8 | 14 × 8 | 112 |
| 9 | 14 × 9 | 126 |
| 10 | 14 × 10 | 140 |
| 11 | 14 × 11 | 154 |
| 12 | 14 × 12 | 168 |
| 13 | 14 × 13 | 182 |
| 14 | 14 × 14 | 196 |
| 15 | 14 × 15 | 210 |
| 16 | 14 × 16 | 224 |
| 17 | 14 × 17 | 238 |
| 18 | 14 × 18 | 252 |
| 19 | 14 × 19 | 266 |
| 20 | 14 × 20 | 280 |
Key Properties of Multiples of 14
- Every multiple of 14 is divisible by both 2 and 7.
- All multiples of 14 are even numbers.
- The difference between any two consecutive multiples of 14 is always 14.
- Multiples of 14 can be positive, zero, or negative (e.g., -14, 0, 14, 28, ...).
- All multiples of 14 are also multiples of its factors (2 and 7). Learn more about Factors of 14 here.
Multiples vs. Factors
| Multiples of 14 | Factors of 14 |
|---|---|
| Generated by multiplying 14 by whole numbers (e.g., 14, 28, 42...) |
Numbers that divide 14 exactly (e.g., 1, 2, 7, 14) |
| Infinite set | Finite set |
| All multiples of 14 are greater than or equal to 14 (except 0 and negatives) | All factors are less than or equal to 14 |
Worked Examples
Example 1: Is 98 a multiple of 14?
- Divide 98 by 14: 98 ÷ 14 = 7.
- Since the result is a whole number, 98 is a multiple of 14.
Example 2: Find the next multiple of 14 after 112.
- 112 ÷ 14 = 8 (So 112 is the 8th multiple).
- Next multiple: 14 × 9 = 126.
Example 3: List all multiples of 14 between 50 and 100.
- List: 56, 70, 84, 98 (as shown in the table above).
Practice Problems
- Write the first 7 multiples of 14.
- Is 140 a multiple of 14? Explain why.
- Find all multiples of 14 between 100 and 200.
- Which is greater: the 10th multiple of 14 or the 8th multiple of 18?
- If a number is a multiple of both 14 and 15, what is the least such number?
Common Mistakes to Avoid
- Confusing multiples with factors (e.g., thinking 7 is a multiple of 14).
- Forgetting to include 14 itself as the smallest positive multiple.
- Thinking only positive numbers are multiples (zero and negatives are also valid multiples).
- Assuming all even numbers are multiples of 14 – only those divisible by 14 count!
Real-World Applications
Multiples of 14 are found in real-life contexts, such as organizing items in groups of 14, sports tournaments with rounds of 14 games, or planning events over weeks (a fortnight = 14 days). Understanding such number patterns is also key in computer science and business scheduling. For more on number patterns, visit Number Patterns.
In this topic, we learned how to recognize and generate multiples of 14, explored their properties, and saw their practical use. Mastering multiples helps students solve problems faster and builds a strong base for topics like the LCM, divisibility, and arithmetic progressions. For more maths help, visit Vedantu and explore related topics such as Multiples, Factors and Multiples, and Factors of 14.
FAQs on Multiples of 14 Explained: Easy Lists & Examples
1. What are the multiples of 14?
Multiples of 14 are numbers obtained by multiplying 14 by any whole number (0, 1, 2, 3, and so on). They represent the result of repeated addition of 14.
2. Is 84 a multiple of 14?
Yes, 84 is a multiple of 14 because 14 x 6 = 84. To check if a number is a multiple of 14, you can divide the number by 14. If the result is a whole number, it's a multiple.
3. How can I find if a number is a multiple of 14?
To determine if a number is a multiple of 14, divide the number by 14. If the division results in a whole number (no remainder), then the number is a multiple of 14. You can also check if it's divisible by both 2 and 7, since 14 = 2 x 7.
4. What is the 18th multiple of 14?
The 18th multiple of 14 is calculated by multiplying 14 by 18: 14 x 18 = 252. Therefore, 252 is the 18th multiple of 14.
5. How are multiples of 14 used in real life?
Multiples of 14 appear in various real-life situations. For example, a fortnight (two weeks) consists of 14 days, so any multiple of 14 represents a number of fortnights. They are also used in scenarios involving groupings, such as arranging 14 items into sets.
6. What can 14 be multiplied by?
14 can be multiplied by any whole number (0, 1, 2, 3, and so on) to produce its multiples. These include 0, 14, 28, 42, 56, and so forth, extending infinitely.
7. What are the factors of 14?
The factors of 14 are the numbers that divide 14 evenly without leaving a remainder. These are 1, 2, 7, and 14. Note that factors are different from multiples.
8. Why is 14 a multiple of 2?
14 is a multiple of 2 because it can be obtained by multiplying 2 by a whole number (2 x 7 = 14). All even numbers are multiples of 2.
9. What are the 18 multiples of 14?
The first eighteen multiples of 14 are: 0, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238. To find more, continue multiplying 14 by consecutive whole numbers.
10. What are the first 10 multiples of 14?
The first ten multiples of 14 are: 0, 14, 28, 42, 56, 70, 84, 98, 112, and 126. These are obtained by multiplying 14 by 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 respectively.
11. Multiples of 14 up to 1000?
To find all multiples of 14 up to 1000, you would repeatedly add 14 or multiply 14 by whole numbers until you reach a product less than or equal to 1000. The largest multiple under 1000 will be 14 multiplied by 71 which equals 994.
12. Multiples of 14 chart?
A multiples of 14 chart would display a sequence of numbers that are multiples of 14, typically arranged in a table format. It would help visually demonstrate the pattern of increasing multiples.
