Divisibility By 6: A Math Guide

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Hey everyone! Let's dive into a common math question: "Which of the following numbers is divisible by 6?" We're going to break down how to easily figure this out, making sure you ace these kinds of problems. This guide is designed to be super clear and helpful, so you'll be a pro in no time.

Understanding Divisibility by 6

Okay, so what does it really mean for a number to be divisible by 6? Well, it means that the number can be divided by 6 without leaving any remainder. Think of it like this: if you can split something into 6 equal groups, and there's nothing left over, then it's divisible by 6. To make things simple, a number is divisible by 6 if it meets two specific criteria: it has to be divisible by both 2 and 3. These are the keys to unlocking this math puzzle!

Let's get into how to easily check these criteria. First, a number is divisible by 2 if it's an even number. This means the last digit of the number is 0, 2, 4, 6, or 8. Simple, right? Next up, the divisibility rule for 3. This one is a little trickier, but still manageable. A number is divisible by 3 if the sum of its digits is divisible by 3. You add up all the digits in the number, and if the total is divisible by 3 (meaning it divides evenly, with no remainder), then the original number is also divisible by 3. Understanding and applying these two rules will make solving the initial question a piece of cake. This combined approach is the secret sauce for determining if a number is divisible by 6, ensuring you can tackle similar problems with confidence. Remembering these rules is your superpower here, so let's put them to work!

Cracking the Code: The Answer

Now, let's look at the options you gave to see which one fits the bill. We'll go through each choice step-by-step. Keep in mind, to be divisible by 6, the number must be both even and the sum of its digits must be divisible by 3. Let's see how this works in practice, shall we?

  • Option A: 174

    • Step 1: Is it even? Yes, the last digit is 4, so it's even.
    • Step 2: Is the sum of digits divisible by 3? 1 + 7 + 4 = 12. And guess what? 12 is divisible by 3. Bingo!
    • Conclusion: Since 174 is both even and the sum of its digits is divisible by 3, 174 is divisible by 6.

  • Option B: 152

    • Step 1: Is it even? Yes, the last digit is 2, so it's even.
    • Step 2: Is the sum of digits divisible by 3? 1 + 5 + 2 = 8. Nope, 8 is not divisible by 3.
    • Conclusion: Since the sum of the digits is not divisible by 3, 152 is not divisible by 6.

  • Option C: 143

    • Step 1: Is it even? No, the last digit is 3, which is not even.
    • Step 2: Does it matter? Not really, since it's not even, it can't be divisible by 6.
    • Conclusion: 143 is not divisible by 6.

  • Option D: 134

    • Step 1: Is it even? Yes, the last digit is 4, so it's even.
    • Step 2: Is the sum of digits divisible by 3? 1 + 3 + 4 = 8. Nope, 8 is not divisible by 3.
    • Conclusion: Since the sum of the digits is not divisible by 3, 134 is not divisible by 6.

Therefore, the correct answer is A) 174. By breaking down each option like this, you can clearly see how the divisibility rules apply.

Tips for Success

To become a divisibility expert, here are a few extra tips and tricks that will help you. Regularly practicing these problems is key. The more you work through them, the quicker you'll get at spotting the patterns. Take some time each day to review similar examples. Another great approach is teaching someone else. Explaining the rules to another person can solidify your own understanding. When you explain a concept, you start thinking about it in different ways, which often leads to a deeper understanding. Also, don't be afraid to make mistakes! Everyone makes mistakes, and it's from those errors that you actually learn. Use any errors as an opportunity to review the rules, understand where you went wrong, and improve your skills. Embrace the challenge, and soon you'll be solving these problems with ease!

Further Practice and Resources

Ready to level up your math skills? Here are some resources and extra practice tips: First off, try working through practice problems online. There are tons of websites and apps that provide interactive quizzes and worksheets. This is a fun and engaging way to test what you have learned and to improve your speed and accuracy. Another great idea is to check out math textbooks and workbooks. These often have sections dedicated to divisibility rules, with step-by-step examples and exercises. Look for books that explain the concepts in detail and offer plenty of practice questions. If you are a visual learner, YouTube channels and online courses with video lessons are super helpful. Many educators create videos that explain math concepts in easy-to-follow ways. Find channels that you enjoy and watch a few videos each week to reinforce your understanding. Make sure you don't forget to practice regularly. Consistent practice is the most important thing. Spend some time each day or a few times a week working through problems. This will help you remember the rules and apply them quickly. Don't worry if it seems difficult at first. With practice, you'll become more confident in your ability to solve these kinds of math problems.

Conclusion

So, there you have it! Understanding divisibility by 6 is not as hard as it might seem. By remembering that a number must be divisible by both 2 and 3, you're well on your way to acing these questions. Keep practicing, keep learning, and you will become a math master in no time! Keep in mind, that math is not just about memorizing rules, it's also about applying those rules and having fun while doing it. Happy calculating, everyone!