What are the first 10 multiples of 8?
The concept of multiples of 8 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.
What Is Multiples of 8?
A multiple of 8 is any number that can be written as 8 multiplied by a whole number. For example, 8, 16, 24, and 32 are all multiples of 8 because you get them by calculating 8 × 1, 8 × 2, 8 × 3, and 8 × 4. You’ll find this concept applied in areas such as multiplication tables, LCM and HCF calculations, and divisibility checks in number theory.
Key Formula for Multiples of 8
Here’s the standard formula: \( \text{Multiple of 8} = 8 \times n \), where n is any whole number (0, 1, 2, 3, ...)
Cross-Disciplinary Usage
Multiples of 8 are not only useful in Maths but also play an important role in Physics (like measuring bytes in Computer Science), logical reasoning, and even in daily life situations such as arranging seats or packing objects. Students preparing for exams like JEE, NEET, and Olympiads will see its relevance in number systems and arithmetic problems.
Step-by-Step Illustration
- Start with the definition:
To find a multiple of 8, choose any whole number (for example, n = 5). - Multiply that number by 8:
8 × 5 = 40 - Final Answer:
40 is a multiple of 8.
List of Multiples of 8 (Up to 100)
| n | 8 × n | Result |
|---|---|---|
| 1 | 8 × 1 | 8 |
| 2 | 8 × 2 | 16 |
| 3 | 8 × 3 | 24 |
| 4 | 8 × 4 | 32 |
| 5 | 8 × 5 | 40 |
| 6 | 8 × 6 | 48 |
| 7 | 8 × 7 | 56 |
| 8 | 8 × 8 | 64 |
| 9 | 8 × 9 | 72 |
| 10 | 8 × 10 | 80 |
Speed Trick or Vedic Shortcut
Here’s a quick shortcut: To check if a number is a multiple of 8, look at its last three digits. If those are divisible by 8, so is the whole number! For example, to check if 2,456 is a multiple of 8, just check 456 ÷ 8 = 57 (no remainder). So, 2,456 is a multiple of 8.
Example Trick: To find the 12th multiple of 8, multiply fast: 8 × 12 = 96.
Tricks like these help during exams. You can learn more in Multiples or get visuals from Table of 8 for instant reference.
Try These Yourself
- Write the first five multiples of 8.
- Check if 56 is a multiple of 8.
- Find all multiples of 8 between 40 and 80.
- Identify which number from 30, 32, 36 is not a multiple of 8.
- What is the 15th multiple of 8?
Frequent Errors and Misunderstandings
- Assuming multiples of 8 are the same as factors of 8.
- Adding 8 repeatedly but missing numbers or skipping by mistake.
- Confusing with the multiples of 4 (all multiples of 8 are multiples of 4, but not the reverse!)
- Mixing up "even number" with "multiple of 8" (Not all even numbers are multiples of 8, but all multiples of 8 are even!)
Relation to Other Concepts
The idea of multiples of 8 connects closely with topics such as multiples of 4 and LCM and HCF. Understanding these helps you solve problems in factors, common multiples, as well as divisibility rules. To clarify "multiples vs factors," check Factors and Multiples.
Classroom Tip
A quick way to remember multiples of 8 is by skip counting: 8, 16, 24, 32, and so on—just add 8 each time. Try saying them out loud or write them as a table for practice. Vedantu’s teachers often use visual patterns and color-coded charts to help learners spot the sequence easily.
Multiples of 8 vs Factors of 8 Table
| Feature | Multiples of 8 | Factors of 8 |
|---|---|---|
| Definition | Products of 8 and whole numbers (8 × n) | Numbers that divide 8 exactly |
| Examples | 8, 16, 24, 32, 40, ... | 1, 2, 4, 8 |
| Infinite? | Yes | No |
| Used for | LCM, finding patterns, division | HCF, dividing into groups |
Wrapping It All Up
We explored multiples of 8—from definition, pattern, calculation tricks, and common mistakes to links with exam topics. Keep practicing with Vedantu for clear concepts and quick problem-solving. For deeper understanding, visit the complete multiples of 8 page or check out Divisibility Rules for more tips. Mastering multiples is fun and useful for every school exam and real life too!
FAQs on Multiples of 8 – Definition, List, Patterns & Practice
1. What are the first 10 multiples of 8?
The first ten multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80. These are obtained by multiplying 8 by each whole number from 1 to 10.
2. How do I find the nth multiple of 8?
To find the nth multiple of 8, simply multiply 8 by n. For example, the 5th multiple is 8 x 5 = 40. This works for any whole number n.
3. Are multiples of 8 always even numbers?
Yes, all multiples of 8 are even numbers. This is because 8 itself is an even number, and the product of any number and an even number is always even.
4. What is the difference between multiples and factors?
Multiples are the results of multiplying a number by whole numbers (e.g., multiples of 8 are 8, 16, 24...). Factors are numbers that divide a given number exactly without leaving a remainder (e.g., factors of 12 are 1, 2, 3, 4, 6, and 12).
5. How can I quickly check if a number is a multiple of 8?
Divide the number by 8. If the division results in a whole number (no remainder), then the number is a multiple of 8.
6. What are some real-life examples where understanding multiples of 8 is useful?
Understanding multiples of 8 is helpful in various situations, such as: calculating the total number of items in groups of 8 (e.g., arranging chairs in rows of 8), working with time (minutes are multiples of 60, which is a multiple of 8), or determining quantities in data storage (bytes, kilobytes).
7. What is the 100th multiple of 8?
The 100th multiple of 8 is 8 x 100 = 800.
8. What are the first five multiples of 8 that are also multiples of 4?
Since 8 is a multiple of 4, all multiples of 8 are also multiples of 4. The first five are: 8, 16, 24, 32, 40.
9. Is 80 a multiple of 8?
Yes, 80 is a multiple of 8 because 80 ÷ 8 = 10.
10. How are multiples of 8 used in finding the Least Common Multiple (LCM)?
When finding the LCM of a set of numbers, including 8, you need to identify the smallest number that is a multiple of all the numbers in the set. Listing multiples of each number can help you find this common multiple.
11. What are some common mistakes students make when working with multiples of 8?
Common mistakes include: confusing multiples with factors; adding 10 instead of multiplying by 8; making calculation errors when multiplying larger numbers by 8; and not understanding the pattern in the sequence of multiples.
12. How do multiples of 8 relate to divisibility rules?
A number is divisible by 8 if its last three digits are divisible by 8. Knowing the multiples of 8 can help you quickly determine if a larger number is divisible by 8.
