Have you ever wondered what the multiples of 6 are and how they can be useful in everyday life? There are infinite multiples of 6, as you can keep multiplying 6 by any natural number endlessly. Understanding multiples is essential not only in mathematics but also in practical applications like scheduling, budgeting, and even cooking.This is because there are an infinite number of natural numbers, leading to an endless list of multiples.
In this article, we will explore the multiples of 6, including how many multiples exist, the smallest multiple, and the natural numbers that fall within this category. We will also provide a 6-times table, use repeated addition to find multiples, and solve examples to reinforce your understanding. By the end, you’ll have a comprehensive grasp of the multiples of 6 and their significance.
Multiples of 6
Multiples of 6 are numbers that can be divided by 6 without leaving a remainder. In simpler terms, a multiple of 6 is the result of multiplying 6 by any natural number. Some examples of multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120…
To find the nth multiple of 6, we can use the formula: nth multiple of 6 = n × 6. For example, the 5th multiple of 6 is 5 × 6 = 30. We can also find multiples of 6 by repeated addition of 6. For instance, 6 + 6 + 6 + 6 + 6 = 30.
Multiples of 6 can be expressed in the form of 6n, where n is a natural number. For example, 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, and so on. The multiplication notation for multiples of 6 is 6 × n, where n is a natural number.
The above multiplication table shows the first 20 multiples of 6 in tabular form. We can see that the multiples of 6 have a difference of 6 between them. This is because the multiplication of 6 with any natural number always results in a multiple of 6.
To find how many multiples of 6 are there between 1 to 100, we can use the formula: number of multiples = (last multiple – first multiple) / 6 + 1. For example, the first multiple of 6 is 6 and the last multiple of 6 less than 100 is 96. Therefore, the number of multiples of 6 between 1 to 100 is (96 – 6) / 6 + 1 = 16.
The smallest multiple of 6 is 6 itself. We can find a few more examples of multiples of 6 by multiplying 6 with natural numbers. For instance, 6 × 2 = 12, 6 × 3 = 18, 6 × 4 = 24, and so on.
In conclusion, multiples of 6 are numbers that can be divided by 6 without leaving a remainder. We can find multiples of 6 by multiplying 6 with natural numbers or by repeated addition of 6. The formula for finding the nth multiple of 6 is n × 6. We can also find the number of multiples of 6 between 1 to 100 using the formula: number of multiples = (last multiple – first multiple) / 6 + 1.
What are the Multiples of 6?
Multiples of 6 are the numbers that can be obtained by multiplying 6 by any whole number. In simpler terms, if you take 6 and multiply it by 1, 2, 3, and so on, you will get a series of numbers multiples of 6. This means that the multiples of 6 include 6, 12, 18, 24, 30, and so forth. The formula to find a multiple of 6 can be expressed as:
Multiple of 6=6×n
where n is any natural number (1, 2, 3, …).
The multiples of 6 up to 100 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
6 Times Table
To effectively understand the multiples of 6, it’s helpful to look at the 6 times table, this table can help you quickly recall the first ten multiples of 6.
| Multiplication of 6 with numbers | Multiples of 6 | Multiplication of 6 with numbers | Multiples of 6 |
| 6 × 1 | 6 | 6 × 11 | 66 |
| 6 × 2 | 12 | 6 × 12 | 72 |
| 6 × 3 | 18 | 6 × 13 | 78 |
| 6 × 4 | 24 | 6 × 14 | 84 |
| 6 × 5 | 30 | 6 × 15 | 90 |
| 6 × 6 | 36 | 6 × 16 | 96 |
| 6 × 7 | 42 | 6 × 17 | 102 |
| 6 × 8 | 48 | 6 × 18 | 108 |
| 6 × 9 | 54 | 6 × 19 | 114 |
| 6 × 10 | 60 | 6 × 20 | 120 |
Free Multiplication table of 6 Worksheet: Download Printable Free
Multiples of 6 by Repeated Addition
Another way to find the multiples of 6 is through repeated addition. For instance, you can start from 0 and keep adding 6:
- Start at 0
- 0 + 6 = 6
- 6 + 6 = 12
- 12 + 6 = 18
- 18 + 6 = 24
- 24 + 6 = 30
- 30 + 6 = 36
Continuing this process, the fifth multiple of 6 is 30, the sixth multiple of 6 is 36.
By continuing this process, you will generate an endless list of multiples of 6, demonstrating that they are spaced evenly apart.
Solved Examples on Multiples of 6
Here are five solved examples on multiples of 6, complete with answers and explanations:
Example 1: Find the 5th Multiple of 6
Question: What is the 5th multiple of 6?
Solution:
To find the 5th multiple of 6, use the formula:
5th Multiple=6×5\text{5th Multiple} = 6 \times 5 5th Multiple=6×5
Calculating this gives:
6×5=306 \times 5 = 30 6×5=30
Answer: The 5th multiple of 6 is 30.
Example 2: Determine if 48 is a Multiple of 6
Question: Is 48 a multiple of 6?
Solution:
To check if 48 is a multiple of 6, divide 48 by 6:
48÷6=848 \div 6 = 8 48÷6=8
Since 8 is a whole number, it confirms that 48 is indeed a multiple of 6.
Answer: Yes, 48 is a multiple of 6.
Example 3: List the First Four Multiples of 6
Question: What are the first four multiples of 6?
Solution:The first four multiples of 6 can be found by multiplying 6 by the first four natural numbers:
- 6×1=66 \times 1 = 66×1=6
- 6×2=126 \times 2 = 126×2=12
- 6×3=186 \times 3 = 186×3=18
- 6×4=246 \times 4 = 246×4=24
Answer: The first four multiples of 6 are 6, 12, 18, and the fourth multiple, 24.
Example 4: Find the 10th Multiple of 6
Question: What is the 10th multiple of 6?
Solution:
Using the formula for multiples, we find:
10th Multiple=6×10\text{10th Multiple} = 6 \times 10 10th Multiple=6×10
Calculating this gives:
6×10=606 \times 10 = 60 6×10=60
Answer: The 10th multiple of 6 is 60.
Example 5: Identify the Smallest Multiple of 6 Greater Than 50
Question: What is the smallest multiple of 6 that is greater than 50?
Solution:
To find this, we can list the multiples of 6 until we find one greater than 50:
- 6 (1)
- 12 (2)
- 18 (3)
- 24 (4)
- 30 (5)
- 36 (6)
- 42 (7)
- 48 (8)
- 54 (9)
The first multiple greater than 50 is 54.
Answer: The smallest multiple of 6 greater than 50 is 54.
Interactive Questions on Multiples of 6
Question 1: What is the 12th multiple of 6?
A) 60
B) 72
C) 48
D) 54
Correct Answer: B) 72
Question 2: Which of the following numbers is a multiple of 6?
A) 28
B) 36
C) 45
D) 50
Correct Answer: B) 36
Question 3: How many multiples of 6 are there between 1 and 50?
A) 8
B) 9
C) 7
D) 10
Correct Answer: B) 9 (The multiples are 6, 12, 18, 24, 30, 36, 42, 48)
Question 4: Which of the following is NOT a multiple of 6?
A) 18
B) 24
C) 34
D) 72
Correct Answer: C) 34
Question 5: What is the sum of the first three multiples of 6?
A) 54
B) 36
C) 48
D) 30
Correct Answer: A) 54 (The first three multiples are 6, 12, and 18; 6 + 12 + 18 = 36)
Frequently Asked Question
Q 1. Rapid Recall of Multiples of 6?
A quick way to recall the multiples of 6 is to memorize the 6 times table. With practice, you will be able to recall them effortlessly.
Q 2. What is the difference between factors and multiples of 6?
Factors of 6 are the numbers you can multiply together to get 6 (1, 2, 3, 6), while multiples of 6 are the result of multiplying 6 by natural numbers (6, 12, 18, …).
Q 3. What are all the multiples of 6？
The multiples of 6 extend infinitely: 6, 12, 18, 24, 30, 36, and so forth. This demonstrates that there are infinite multiples of 6, as you can keep multiplying 6 by any natural number endlessly.
Q 4. What is the least common multiples of 6 and 8?
Common multiples of two numbers (like 6 and 8) are numbers that are multiples of both. For example, 24 is a common multiple of 6 and 8.
Conclusion
Understanding the multiples of 6 is not just about memorizing numbers; it’s about recognizing their relevance in various real-world scenarios. Whether you’re helping your child with math homework or trying to manage time efficiently, knowing the multiples of 6 can be incredibly beneficial. If you’re interested in deepening your mathematical skills, consider enrolling in WuKong Math courses, where you can explore these concepts further and enhance your understanding of mathematics: WuKong Math.
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