Divisible Number Between 60 And 80: How To Find It?

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Hey guys! Ever found yourself scratching your head over a math problem that seems trickier than it actually is? Well, today, we're diving into a super common type of question: finding a number within a specific range that's divisible by another number. Specifically, we're tackling the question: "What number between 60 and 80 is divisible?" Sounds like a puzzle, right? Don't worry; we'll break it down step by step, making it super easy to understand. So, grab your thinking caps, and let's get started!

Understanding Divisibility

Before we jump into solving our main question, let's quickly refresh our understanding of divisibility. In simple terms, a number is divisible by another number if, after dividing, you get a whole number (no remainders!). For example, 10 is divisible by 2 because 10 ÷ 2 = 5, a whole number. But 10 is not divisible by 3 because 10 ÷ 3 = 3 with a remainder of 1. So, when we're looking for a number between 60 and 80 that's divisible, we're essentially looking for a number that can be divided by another number without leaving any leftovers. This concept is crucial, because understanding divisibility is the first step to solving this kind of problem. Think of it like this: imagine you have a bunch of candies, and you want to share them equally among your friends. If the number of candies is divisible by the number of friends, everyone gets the same amount, and there are no candies left over. If it's not divisible, someone will end up with extra, which isn't fair, right? In math terms, this "fair sharing" is what divisibility is all about. Now that we've got a solid grasp of what it means for a number to be divisible, we can move on to thinking about different strategies for finding our mystery number between 60 and 80. We could go through each number one by one, checking if it's divisible by something, or we can be a bit smarter about it. We'll explore some clever techniques in the next sections, so stay tuned! Remember, math isn't about just memorizing rules; it's about understanding the "why" behind them. Once you get that, you'll be able to tackle all sorts of problems with confidence. And that's exactly what we're aiming for today. Let’s get into the nitty-gritty of our specific problem and see how we can find the divisible number we're searching for.

Identifying Potential Divisors

Okay, so we know we're looking for a number between 60 and 80 that's divisible. But divisible by what? That's the next key question we need to answer. Identifying potential divisors will help us narrow down our search significantly. We need to think about numbers that could reasonably divide into something between 60 and 80. Obvious candidates include 2, 3, 4, 5, 6, and so on. But let's think a bit strategically here. If a number is divisible by a larger number, it's less likely to fall within our relatively small range of 60 to 80. For instance, a number divisible by 20 would need to be at least 20, 40, 60, 80... See? Only a couple of those fit our range. So, focusing on smaller divisors is a smart move. Let's consider the properties of numbers divisible by some of these smaller divisors:

  • Divisible by 2: Any even number is divisible by 2. This is a super helpful rule, as it immediately gives us a bunch of potential candidates within our 60-80 range. Remember, even numbers are those that end in 0, 2, 4, 6, or 8.
  • Divisible by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. This one's a bit trickier, but still manageable. For example, 63 (6 + 3 = 9) is divisible by 3, while 64 (6 + 4 = 10) is not. 66 (6+6=12) is also divisible by 3.
  • Divisible by 5: Numbers divisible by 5 end in either 0 or 5. This is another easy rule to remember and apply. So, in our range, 60, 65, 70, 75, and 80 are all divisible by 5.
  • Divisible by 10: Numbers divisible by 10 end in 0. This is the simplest rule of all! Within our range, that gives us 60, 70, and 80.

By understanding these divisibility rules, we've already made our task much easier. We've identified a pool of potential numbers and have some simple ways to check if they fit the bill. This is a crucial step in identifying potential divisors. We're not just blindly guessing; we're using our math knowledge to make informed decisions. Now, let's move on to actually testing some numbers and see if we can find our divisible number. We've got some clues; let's put them to use!

Testing Numbers Within the Range

Alright, we've got our range (60 to 80), and we've identified some potential divisors (2, 3, 5, 10, and maybe a few others). Now comes the fun part: putting our detective hats on and testing some numbers! We're going to systematically go through numbers within our range and see if they're divisible by any of the divisors we've identified. Remember, our goal is to find at least one number that fits the criteria. Let's start by considering even numbers since they're divisible by 2, which is a pretty straightforward divisor. The even numbers between 60 and 80 are: 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, and 80. That's a good starting list! Now, let's see which of these are divisible by other numbers as well. For example:

  • 60: We know 60 is divisible by 2 (it's even), 3 (6 + 0 = 6, which is divisible by 3), 5 (ends in 0), and 10 (ends in 0). Wow, 60 is quite a versatile number!

  • 62: Divisible by 2, but not by 3 or 5.

  • 64: Divisible by 2, but not by 3 or 5.

  • 65: Let's consider the numbers ending with 5. It is not divisible by 2, 3, or 10, but it is divisible by 5.

  • 66: Divisible by 2 and 3 (6 + 6 = 12, which is divisible by 3). It is also divisible by 6, as it is divisible by both 2 and 3.

  • 68: Divisible by 2, but not by 3 or 5.

  • 69: Let's also take a quick detour to consider numbers divisible by 3. It is not divisible by 2 or 5, but it is divisible by 3.

  • 70: Divisible by 2, 5, and 10. Another strong contender!

  • 72: Divisible by 2 and 3 (7 + 2 = 9, which is divisible by 3). It is also divisible by 4, 6 and 8.

  • 74: Divisible by 2, but not by 3 or 5.

  • 75: Divisible by 5 and 3 (7 + 5 = 12, which is divisible by 3).

  • 76: Divisible by 2, but not by 3 or 5.

  • 78: Divisible by 2 and 3 (7 + 8 = 15, which is divisible by 3).

  • 80: Divisible by 2, 5, and 10.

As you can see, testing numbers within the range systematically helps us identify the ones that are divisible by various numbers. We've already found several numbers that fit the bill! This process might seem a bit tedious, but it's a reliable way to solve the problem. And, more importantly, it helps us understand how divisibility works in practice. Now that we've tested a bunch of numbers, let's take a step back and think about how we can choose the "best" answer, depending on what the question is really asking.

Choosing the Right Answer

So, we've done the hard work of identifying several numbers between 60 and 80 that are divisible. But here's a crucial point: the question might be a little ambiguous. When it asks, "What number between 60 and 80 is divisible?" it might be looking for any number that's divisible by something, or it might be looking for a number that's divisible by a specific number. This is where reading the question carefully becomes super important. Let's consider a couple of scenarios:

  • Scenario 1: Any Divisible Number If the question simply wants any number that's divisible, then we have a ton of answers! As we saw in the previous section, 60, 62, 64, 65, 66, 68, 70, 72, 74, 75, 76, 78, and 80 all fit the bill because they're divisible by at least one number (usually 2, 3, 5, or 10). In this case, you could choose any of these numbers as your answer. 60 is divisible by many numbers, making it a strong contender. But so are 66, 70, 72, and others.

  • Scenario 2: Divisible by a Specific Number Now, what if the question is a bit more specific? What if it's secretly asking, "What number between 60 and 80 is divisible by 7?" (We didn't explicitly check for divisibility by 7 before). Or maybe it's asking, "What's the largest number between 60 and 80 that's divisible by 6?" In these cases, we need to do a little extra digging. To find a number divisible by 7, we could quickly run through the multiples of 7: 7 x 9 = 63, 7 x 10 = 70, 7 x 11 = 77. Aha! 70 and 77 are in our range. 77 is divisible by 7, so that would be our answer in this scenario. For the largest number divisible by 6, we could start from 80 and work our way down, checking for divisibility by 6. 78 is divisible by 6 (78 / 6 = 13), so that would be our answer here. This demonstrates the importance of choosing the right answer. It's not just about finding a divisible number; it's about finding the one that best fits the specific question being asked. So, always read the question carefully and make sure you understand exactly what it's looking for. Sometimes, the trickiest part of a math problem isn't the math itself, but understanding what the question is really asking! To recap, we've explored various numbers within our range and considered different divisibility rules. We've also highlighted the importance of understanding the question's intent. Now, let's wrap things up with a quick summary and some final thoughts.

Conclusion

So, guys, we've taken a deep dive into the question of finding a divisible number between 60 and 80. We've covered a lot of ground, from understanding the basic concept of divisibility to identifying potential divisors, testing numbers within the range, and finally, the crucial step of choosing the right answer based on the question's specific requirements. Remember, the key takeaway here isn't just finding one specific answer, but the process we used to get there. We learned how to think systematically, apply divisibility rules, and carefully interpret the question being asked. These are valuable skills that will help you tackle all sorts of math problems, not just this one. Math isn't about memorizing formulas; it's about developing a logical way of thinking and problem-solving. And that's exactly what we've practiced today. Whether you were looking for any divisible number or one divisible by a specific number, we've equipped you with the tools and knowledge to find it. So, next time you encounter a similar question, don't panic! Just break it down step by step, use the strategies we've discussed, and you'll be well on your way to finding the solution. And hey, if you get stuck, remember to come back and revisit this guide. We've covered all the essential steps to solving this type of problem. Happy calculating, and keep exploring the fascinating world of numbers! Math can be challenging, but it's also incredibly rewarding when you crack the code and find the answer. Keep practicing, keep questioning, and most importantly, keep having fun with it!