What Are the First 20 Multiples of 42?
The concept of Multiples of 42 is an important part of number theory and arithmetic. Learning how to identify, list, and use multiples of 42 helps students solve a variety of mathematics problems related to patterns, division, algebra, and more. This concept is highly relevant for school exams and quick revision as well as in competitive exams where number properties play a key role.
Understanding Multiples of 42
A multiple of 42 is any number that results from multiplying 42 by a whole number (integer). In other words, if you see 42 in the multiplication table or skip-counting sequence, that number is a multiple of 42. For example, 42, 84, 126, and 168 are all multiples of 42, as they can be written as \( 42 \times 1 \), \( 42 \times 2 \), \( 42 \times 3 \), and \( 42 \times 4 \) respectively. This foundational idea is often used in topics like divisibility, factors, least common multiples (LCM), and arithmetic series.
Formula for Multiples of 42
To find a multiple of 42, use this formula:
Multiple = \( 42 \times n \)
Where \( n \) is any whole number (1, 2, 3, 4, ...). For example, to get the 5th multiple, use \( n = 5 \):
\( 42 \times 5 = 210 \).
First 20 Multiples of 42 (Chart)
Here's a quick chart showing the first 20 multiples of 42 for study and reference:
| n | 42 × n | Value |
|---|---|---|
| 1 | 42 × 1 | 42 |
| 2 | 42 × 2 | 84 |
| 3 | 42 × 3 | 126 |
| 4 | 42 × 4 | 168 |
| 5 | 42 × 5 | 210 |
| 6 | 42 × 6 | 252 |
| 7 | 42 × 7 | 294 |
| 8 | 42 × 8 | 336 |
| 9 | 42 × 9 | 378 |
| 10 | 42 × 10 | 420 |
| 11 | 42 × 11 | 462 |
| 12 | 42 × 12 | 504 |
| 13 | 42 × 13 | 546 |
| 14 | 42 × 14 | 588 |
| 15 | 42 × 15 | 630 |
| 16 | 42 × 16 | 672 |
| 17 | 42 × 17 | 714 |
| 18 | 42 × 18 | 756 |
| 19 | 42 × 19 | 798 |
| 20 | 42 × 20 | 840 |
How to Find Multiples of 42
To find the multiples of 42, follow these steps:
- Start with the number 42.
- Add 42 to get the next multiple (42 + 42 = 84).
- Continue adding 42 each time, or multiply 42 by increasing whole numbers (n = 1, 2, 3, etc).
For example, for n = 6:
\( 42 \times 6 = 252 \)
Multiples of 42 in Pairs
Sometimes, students are asked for multiples of 42 in pairs, which means showing both the multiplier and the result. This helps identify patterns:
| n | Multiple (42 × n) | Pair (n, 42 × n) |
|---|---|---|
| 1 | 42 | (1, 42) |
| 2 | 84 | (2, 84) |
| 3 | 126 | (3, 126) |
| 4 | 168 | (4, 168) |
| 5 | 210 | (5, 210) |
You can continue this pattern for any natural number n.
Worked Examples: Multiples of 42
Example 1:
Find the 12th multiple of 42.
- \( 42 \times 12 = 504 \)
Example 2:
Is 294 a multiple of 42?
- Divide 294 by 42: \( 294 \div 42 = 7 \)
- Answer: Yes, since the result is a whole number (7).
Example 3:
What is the 100th multiple of 42?
- \( 42 \times 100 = 4200 \)
Practice Problems
- List the first seven multiples of 42.
- Is 630 a multiple of 42?
- Find the multiple of 42 that is just above 500.
- Which is greater, the 8th multiple of 42 or the 10th multiple of 42? By how much?
- What is the 25th multiple of 42?
Common Mistakes to Avoid
- Confusing multiples with factors. Remember: multiples are the result of multiplying, factors are what divide the number.
- Assuming all multiples of 42 are odd. In fact, they are all even because 42 is even.
- Forgetting to use only whole numbers for n (do not use fractions or zero if looking for positive multiples).
- Not checking the division remainder—if a number divided by 42 does not yield a whole number, it is NOT a multiple.
Real-World Applications
Multiples of 42 appear in scheduling, packaging, and any scenario where you group items in equal sets of 42. For example:
- Suppose each box holds 42 pencils. To know how many pencils are in 6 boxes, find \( 42 \times 6 = 252 \).
- Sports teams: If each cricket match has 42 overs, the total balls bowled is a multiple of 42.
- Arranging chairs/people into groups of 42 for events or competitions.
At Vedantu, we make learning about patterns and multiples like these simple and engaging for all students.
To master similar concepts, check out the multiplication table of 42 or how to differentiate factors of 42 from multiples. You can read more about finding common multiples and learn about LCM for advanced problem-solving.
In this topic, you learned how to identify and list multiples of 42, use the multiplication formula, and apply this knowledge in everyday situations. Understanding multiples can strengthen your foundation in number theory and improve your problem-solving skills both in school mathematics and in real-world scenarios. Practice regularly and explore more Maths topics with Vedantu for a clear and confident understanding!
FAQs on Multiples of 42 Explained with Easy Examples
1. What are the first ten multiples of 42?
The first ten multiples of 42 are obtained by multiplying 42 by the integers 1 through 10. They are: 42, 84, 126, 168, 210, 252, 294, 336, 378, and 420.
2. Is 42 a multiple of 7?
Yes, 42 is a multiple of 7 because 7 multiplied by 6 equals 42 (7 x 6 = 42). This means 42 is divisible by 7 without any remainder. This is important for understanding divisibility and number patterns.
3. What is the difference between factors and multiples of 42?
Factors of 42 are numbers that divide 42 without leaving a remainder (e.g., 1, 2, 3, 6, 7, 14, 21, 42). Multiples of 42 are numbers obtained by multiplying 42 by any integer (e.g., 42, 84, 126, etc.). Factors are smaller than or equal to the number, while multiples are greater than or equal to the number.
4. What are the common multiples of 42 and 28?
Common multiples of 42 and 28 are numbers that are multiples of both 42 and 28. The first few common multiples are 84, 168, 252, etc. Finding the least common multiple (LCM) is a key concept in this area. The LCM of 42 and 28 is 84.
5. How can I quickly check if a number is a multiple of 42?
To quickly check if a number is a multiple of 42, verify if it's divisible by both 2 and 21 (since 42 = 2 x 21). If the number is even and also divisible by 21, then it's a multiple of 42. Use divisibility rules for 2 and 21 for faster calculation. Understanding divisibility rules helps.
6. What are multiples of 42 in pairs?
Multiples of 42 in pairs refer to representing multiples as ordered pairs (n, 42n), where 'n' is an integer. For example: (1, 42), (2, 84), (3, 126), and so on. This helps visualize the relationship between the integer and its corresponding multiple of 42. This is helpful in pattern recognition.
7. What are the multiples of 42 up to 1000?
To find the multiples of 42 up to 1000, you can repeatedly add 42 or use the formula 42n (where n is an integer). The multiples would be 42, 84, 126,... up to the largest multiple less than or equal to 1000. The last multiple will be 987(42 x 23). Knowing the multiplication table can speed up this process.
8. What are common multiples of 42?
Common multiples of 42 are numbers that are multiples of 42 and at least one other number. For example, if you consider 42 and 21, some common multiples are 42, 84, 126, etc. Finding the least common multiple (LCM) helps identify the smallest of these common multiples.
9. What are the first ten multiples of 42 and their pairs?
The first ten multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378, 420. Their pairs (n, 42n) would be (1,42), (2,84), (3,126), (4,168), (5,210), (6,252), (7,294), (8,336), (9,378), (10,420). This representation highlights the relationship between the multiplier and the resulting multiple.
10. What are the multiples of 420?
The multiples of 420 are numbers obtained by multiplying 420 by any whole number (integer). For example, the first few multiples are 420, 840, 1260, 1680, and so on. This concept is similar to other multiples but involves a larger starting number.
