How to Find the Multiples of 42 Step by Step
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 Clear Examples
1. What are the multiples of 42?
The multiples of 42 are the numbers you get when you multiply 42 by whole numbers.
They are found using the pattern:
42 × n, where n = 1, 2, 3, 4, ...
- 42 × 1 = 42
- 42 × 2 = 84
- 42 × 3 = 126
- 42 × 4 = 168
- 42 × 5 = 210
2. How do you find the multiples of 42?
You can find the multiples of 42 by multiplying 42 by consecutive whole numbers.
Follow these steps:
- Start with 42 × 1
- Then calculate 42 × 2, 42 × 3, 42 × 4, and so on
- Each result is a multiple of 42
42 × 6 = 252, so 252 is a multiple of 42.
3. What is the formula for multiples of 42?
The formula for the multiples of 42 is 42n, where n is a whole number.
This means:
- If n = 1, multiple = 42
- If n = 2, multiple = 84
- If n = 10, multiple = 420
4. What are the first 10 multiples of 42?
The first 10 multiples of 42 are obtained by multiplying 42 by numbers from 1 to 10.
- 42 × 1 = 42
- 42 × 2 = 84
- 42 × 3 = 126
- 42 × 4 = 168
- 42 × 5 = 210
- 42 × 6 = 252
- 42 × 7 = 294
- 42 × 8 = 336
- 42 × 9 = 378
- 42 × 10 = 420
5. Is 210 a multiple of 42?
Yes, 210 is a multiple of 42 because 210 ÷ 42 = 5.
Since the division gives a whole number:
- 210 ÷ 42 = 5
6. How do you check if a number is a multiple of 42?
A number is a multiple of 42 if it is divisible by 42 without leaving a remainder.
To check:
- Divide the number by 42
- If the remainder is 0, it is a multiple
7. What is the smallest multiple of 42?
The smallest positive multiple of 42 is 42.
This is because:
- 42 × 1 = 42
8. Are multiples of 42 always even?
Yes, multiples of 42 are always even numbers because 42 itself is even.
Since 42 = 2 × 21:
- Any multiple of 42 contains the factor 2
- Therefore, every multiple is divisible by 2
9. What is the difference between factors and multiples of 42?
The difference is that factors of 42 divide 42 exactly, while multiples of 42 are numbers obtained by multiplying 42.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Multiples of 42: 42, 84, 126, 168, ...
10. What is the least common multiple (LCM) of 42 and 6?
The LCM of 42 and 6 is 42 because 42 is the smallest number divisible by both.
Prime factorization method:
- 42 = 2 × 3 × 7
- 6 = 2 × 3
2 × 3 × 7 = 42
So, 42 is the least common multiple.
