Which Number Is A Multiple Of 6 And 8 Solution Explained
Introduction
In the realm of mathematics, understanding multiples is fundamental. Multiples form the bedrock of numerous mathematical concepts, including division, factorization, and number patterns. When we talk about a multiple of a number, we're essentially referring to the result of multiplying that number by an integer. This exploration delves into the concept of multiples, specifically focusing on identifying a number that is a multiple of both 6 and 8. Let's embark on a mathematical journey to uncover the answer.
The question at hand presents us with a multiple-choice scenario: Which number is a multiple of both 6 and 8? The options given are 18, 3, and 24. To accurately determine the solution, we need to understand what it means for a number to be a multiple of another. A number is considered a multiple of another if it can be obtained by multiplying the latter by an integer. For instance, 12 is a multiple of 3 because 3 multiplied by 4 equals 12. Similarly, 20 is a multiple of 5 because 5 multiplied by 4 equals 20. With this understanding, let's examine each option and see if it fits the criteria of being a multiple of both 6 and 8.
To methodically determine the solution, we must assess each option against the criteria of being a multiple of both 6 and 8. This entails examining whether the given number can be evenly divided by both 6 and 8, leaving no remainder. If a number satisfies this condition, it qualifies as a multiple of both 6 and 8. Let's dissect each option to ascertain which one meets this requirement. By systematically analyzing each choice, we can confidently identify the number that aligns with the multiple criteria for both 6 and 8.
Dissecting the Options
1. Examining 18
The first option we encounter is 18. To determine if 18 is a multiple of 6, we perform the division: 18 ÷ 6 = 3. This calculation reveals that 18 is indeed a multiple of 6, as it can be evenly divided by 6 with no remainder. However, to satisfy the question's requirement, 18 must also be a multiple of 8. Let's investigate this aspect.
When we attempt to divide 18 by 8, we get 18 ÷ 8 = 2 with a remainder of 2. This indicates that 18 cannot be evenly divided by 8, meaning it is not a multiple of 8. Consequently, 18 fails to meet the criterion of being a multiple of both 6 and 8. Therefore, we can eliminate 18 as the correct answer. Understanding why 18 does not fit the criteria is crucial in narrowing down our options and progressing towards the accurate solution. The process of elimination is a valuable tool in problem-solving, especially in multiple-choice scenarios.
2. Evaluating 3
Next, we consider the number 3. To assess whether 3 is a multiple of 6, we attempt to divide 3 by 6. However, 3 is smaller than 6, making it impossible to divide 3 evenly by 6. This indicates that 3 is not a multiple of 6. Since 3 fails to meet the initial criterion of being a multiple of 6, it automatically disqualifies as a solution to the question. We don't even need to check if it's a multiple of 8 because it has already failed the first test. The fundamental understanding of multiples and divisibility allows us to quickly eliminate options that don't fit the criteria, streamlining the problem-solving process. This efficient approach saves time and effort, enabling us to focus on the remaining possibilities.
3. Unveiling 24
Finally, we arrive at the number 24. To determine if 24 is a multiple of 6, we perform the division: 24 ÷ 6 = 4. This calculation confirms that 24 is indeed a multiple of 6, as it can be evenly divided by 6 with no remainder. Now, we must assess whether 24 also satisfies the condition of being a multiple of 8. Let's proceed with the division.
When we divide 24 by 8, we get 24 ÷ 8 = 3. This result demonstrates that 24 can be evenly divided by 8, with no remainder. Thus, 24 is a multiple of 8. Having established that 24 is a multiple of both 6 and 8, we can confidently conclude that it is the correct answer to the question. The ability to methodically apply the definition of multiples and divisibility rules is essential in solving such mathematical problems. This systematic approach ensures accuracy and clarity in our reasoning.
Conclusion
In conclusion, among the given options, 24 stands out as the number that is a multiple of both 6 and 8. This determination was made through a systematic analysis of each option, applying the fundamental concept of multiples and divisibility. Understanding what it means for a number to be a multiple of another is crucial in tackling various mathematical problems, including those involving factorization, division, and number patterns. The ability to identify multiples accurately is a cornerstone of mathematical proficiency.
The process of solving this problem underscores the importance of methodical problem-solving in mathematics. By systematically evaluating each option against the given criteria, we were able to eliminate incorrect answers and arrive at the correct solution. This step-by-step approach not only enhances accuracy but also fosters a deeper understanding of the underlying mathematical principles. The ability to break down complex problems into manageable steps is a valuable skill that extends beyond mathematics, benefiting various aspects of life.
Furthermore, this exercise reinforces the significance of mathematical literacy in everyday life. The concept of multiples is not confined to textbooks and classrooms; it permeates various real-world scenarios, from calculating quantities and proportions to understanding financial transactions and time management. A solid grasp of mathematical concepts, such as multiples, empowers individuals to make informed decisions and navigate the complexities of the world around them. Therefore, continuous engagement with mathematical concepts is essential for personal and professional growth. The quest to understand numbers and their relationships is a journey that yields profound insights and practical skills.
