Multiples of 7 from 1 to 100 with Table & Shortcuts
The concept of multiple of 7 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding multiples helps with skip counting, divisibility tests, times tables, and efficient mental arithmetic. Mastering this concept prepares students for a variety of math problems and competitive exams.
What Is a Multiple of 7?
A multiple of 7 is any number that can be divided exactly by 7, with no remainder. In other words, if you multiply 7 by any integer (positive, negative, or zero), you get a multiple of 7. You’ll find this concept applied in areas such as multiplication tables, divisibility rules, and arithmetic progressions.
Key Formula for Multiple of 7
Here’s the standard formula: \( \text{Multiple of 7} = 7 \times n \)
where n is an integer (1, 2, 3, … or 0, -1, -2, …).
List of Multiples of 7 (1 to 20)
| n | 7 × n | Multiple of 7 |
|---|---|---|
| 1 | 7 × 1 | 7 |
| 2 | 7 × 2 | 14 |
| 3 | 7 × 3 | 21 |
| 4 | 7 × 4 | 28 |
| 5 | 7 × 5 | 35 |
| 6 | 7 × 6 | 42 |
| 7 | 7 × 7 | 49 |
| 8 | 7 × 8 | 56 |
| 9 | 7 × 9 | 63 |
| 10 | 7 × 10 | 70 |
| 11 | 7 × 11 | 77 |
| 12 | 7 × 12 | 84 |
| 13 | 7 × 13 | 91 |
| 14 | 7 × 14 | 98 |
| 15 | 7 × 15 | 105 |
| 16 | 7 × 16 | 112 |
| 17 | 7 × 17 | 119 |
| 18 | 7 × 18 | 126 |
| 19 | 7 × 19 | 133 |
| 20 | 7 × 20 | 140 |
How to Find Multiples of 7
- Start with 7 and multiply by 1.
7 × 1 = 7 - Increase the multiplier by 1 each time.
7 × 2 = 14, 7 × 3 = 21, and so on. - Keep multiplying for as many multiples as needed.
For example: 7 × 15 = 105
Divisibility Rule and Speed Tricks for Multiples of 7
Want to check if a number is a multiple of 7? Try this speed trick:
- Double the last digit and subtract it from the rest of the number.
Example: Is 203 a multiple of 7?Double 3 (last digit): 3 × 2 = 6. Subtract from 20: 20 - 6 = 14. - If the answer is a multiple of 7 (14 is), so is the original number.
This quick rule helps in mental math and competitive tests. Practice with more examples to get faster! Vedantu’s live quizzes spotlight such shortcuts for exam speed.
Step-by-Step Illustration
- Question: Is 77 a multiple of 7?
2. 77 ÷ 7 = 11 (no remainder).
3. So, 77 is a multiple of 7.
Try These Yourself
- Write the first five multiples of 7.
- Check if 56 is a multiple of 7.
- Find all multiples of 7 between 30 and 60.
- Identify numbers which are not multiples of 7: 21, 25, 28, 32.
Difference Between Multiple and Factor of 7
| Multiples of 7 | Factors of 7 |
|---|---|
| Numbers like 7, 14, 21, 28, ... (goes on) | Only 1 and 7 |
| Always greater than or equal to 7 (unless negative) | Always less than or equal to 7 |
Relation to Other Concepts
The idea of multiple of 7 connects closely with topics such as factors of 7 and LCM and HCF. Mastering multiples helps with addition, subtraction, and solving equations involving divisibility in later classes.
Frequent Errors and Misunderstandings
- Assuming multiples of 7 means numbers less than 7 (actually, they are equal to or greater than 7 or can be negative).
- Confusing factors with multiples (factors of 7 are only 1 and 7, not unlimited).
- Forgetting that zero and negative numbers can also be multiples of 7. E.g., -14, 0, and -21 are multiples of 7.
Classroom Tip
A fast way to remember multiples of 7 is by skip counting: 7, 14, 21, 28, ... Keep adding 7 each time. Create your own “7 times table” poster for your study room! Vedantu’s teachers often use songs, claps, and charts to help students memorize these patterns.
Wrapping It All Up
We explored multiple of 7 —from the definition, key formula, lists, speed tricks, steps, common mistakes, and its links to other math chapters. Keep practicing with Vedantu and try solving new problems every day to become confident in working with multiples of 7 and other numbers.
Related Math Topics
FAQs on Multiple of 7: Definition, List, Rules, and Examples
1. What is a multiple of 7?
A multiple of 7 is any number that can be obtained by multiplying 7 by an integer. This means it's a number that is exactly divisible by 7, leaving no remainder. For example, 14, 21, and 28 are all multiples of 7 because 7 x 2 = 14, 7 x 3 = 21, and 7 x 4 = 28.
2. How do you find multiples of 7?
To find multiples of 7, simply multiply 7 by any integer (whole number). You can start with 7 × 1 = 7, then 7 × 2 = 14, 7 × 3 = 21, and so on. You can also use skip counting by 7s.
3. What are the first ten multiples of 7?
The first ten multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, and 70.
4. Is 35 a multiple of 7?
Yes, 35 is a multiple of 7 because 7 × 5 = 35.
5. Is -7 a multiple of 7?
Yes, -7 is a multiple of 7 because 7 × -1 = -7. Negative numbers can also be multiples.
6. What are the multiples of 7 between 1 and 100?
The multiples of 7 between 1 and 100 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98.
7. How many multiples of 7 are there between 100 and 1000?
There are 128 multiples of 7 between 100 and 1000. To find this, divide 1000 by 7 (approximately 142), and 100 by 7 (approximately 14). Subtract the results (142 - 14 = 128).
8. What is a quick way to check if a number is a multiple of 7?
There are divisibility rules for 7, but they can be more complex than for other numbers. One method is to double the last digit and subtract it from the remaining digits. If the result is divisible by 7, then the original number is also divisible by 7. For example, for 91: (9 - (1 x 2)) = 7, which is divisible by 7, therefore 91 is a multiple of 7. This method works for larger numbers as well. Repeated application may be necessary.
9. What is the difference between factors and multiples?
Factors are numbers that divide evenly into a given number, while multiples are numbers that result from multiplying a given number by an integer. 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.
10. Are there negative multiples of 7?
Yes, any number multiplied by 7 will result in a multiple of 7, so the product can also be negative. For example, -14, -21, and -28 are all negative multiples of 7.
11. Is zero a multiple of 7?
Yes, zero (0) is a multiple of 7 because 7 multiplied by 0 equals 0.
12. How are multiples of 7 used in real life?
Multiples of 7 appear in various real-world scenarios, such as calculating weeks (7 days), scheduling events recurring every 7 days, or in certain patterns or sequences within data analysis.
