Finding Divisor N: Solve 391 ÷ N = 21 (Remainder 13)

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Hey guys! Let's break down this math problem together. We're trying to find a divisor, n, given that when 391 is divided by n, the result is 21 with a remainder of 13. Sounds a bit tricky, right? Don't worry, we'll get through it step by step. Understanding the core concept of division and remainders is key here. Essentially, we need to figure out what number n can fit into 391 a total of 21 times, leaving 13 leftover. This involves a bit of algebraic thinking and some good old arithmetic. So, grab your pencils and let's dive in!

Understanding the Problem

Alright, before we start crunching numbers, let's make sure we really understand what the question is asking. We're told that when 391 is divided by some number n, we get 21 with a remainder of 13. Mathematically, we can express this as:

391 = 21n + 13

This equation is super important because it sets the foundation for solving the problem. It tells us that 391 is equal to 21 times the divisor (n) plus the remainder (13). Our mission is to isolate n and find its value. To do this, we need to manipulate the equation using basic algebraic principles. Think of it like a puzzle – we need to rearrange the pieces until we reveal the hidden number. First, we'll subtract the remainder from both sides of the equation. This will help us simplify the equation and get closer to isolating n. Then, we'll divide both sides by 21. Doing so will finally reveal the value of n. Make sense? Great, let's move on to the next step where we'll actually start solving the equation. This is where the real fun begins!

Solving for n

Okay, let's get down to business! We've already established our equation:

391 = 21n + 13

The first step is to subtract 13 from both sides of the equation. This will help us isolate the term with n:

391 - 13 = 21n + 13 - 13

This simplifies to:

378 = 21n

Now, to find n, we need to divide both sides of the equation by 21:

378 / 21 = (21n) / 21

This gives us:

n = 18

So, the divisor n is 18. We can check our answer by plugging it back into the original equation:

391 = (21 * 18) + 13

391 = 378 + 13

391 = 391

Yep, it checks out! This confirms that our solution is correct. n is indeed 18. Wasn't that satisfying? Solving for n involves understanding the relationship between the dividend, divisor, quotient, and remainder, and then using algebraic manipulation to isolate the unknown variable. Now that we've found n, let's take a moment to reflect on what we've learned and how we can apply this knowledge to similar problems.

Verification and Conclusion

To be absolutely sure we've nailed it, let's double-check our work. We found that n = 18. This means that when we divide 391 by 18, we should get a quotient of 21 and a remainder of 13. Let's perform the division:

391 ÷ 18 = 21 with a remainder of 13

Indeed, it works perfectly! This confirms that our solution is correct. Therefore, the divisor n is 18. This process of verifying the solution is crucial in mathematics. It ensures that we haven't made any errors along the way and that our answer is accurate. In conclusion, by understanding the relationship between the dividend, divisor, quotient, and remainder, and by using basic algebraic principles, we were able to successfully solve for n. Remember, the key is to break down the problem into smaller, more manageable steps. This makes it easier to understand and solve. With practice, you'll become more confident in your ability to tackle similar problems. Keep practicing and you'll be a math whiz in no time!

Additional Practice Problems

Want to keep those math muscles flexed? Here are a few more practice problems similar to the one we just solved:

  1. Find the divisor m, if 527 ÷ m = 17 (remainder 1).
  2. Find the divisor p, if 800 ÷ p = 32 (remainder 16).
  3. Find the divisor q, if 410 ÷ q = 13 (remainder 8).

Try solving these problems using the same method we used earlier. Remember to first express the problem as an equation, then isolate the divisor by subtracting the remainder and dividing by the quotient. Don't forget to verify your answer by plugging it back into the original equation. Solving these practice problems will help you reinforce your understanding of the concepts and improve your problem-solving skills. The more you practice, the more comfortable you'll become with these types of problems. So, grab a pen and paper and give these problems a try! You got this!

Tips for Solving Similar Problems

Here are some handy tips to keep in mind when tackling similar problems in the future:

  • Always start by writing down the given information and expressing the problem as an equation. This will help you visualize the relationship between the dividend, divisor, quotient, and remainder.
  • Isolate the divisor by subtracting the remainder from the dividend and then dividing by the quotient. This will give you the value of the divisor.
  • Verify your answer by plugging it back into the original equation. This will ensure that your solution is correct.
  • Practice, practice, practice! The more you practice, the more comfortable you'll become with these types of problems.
  • Don't be afraid to ask for help if you're stuck. There are plenty of resources available online and in your community that can help you with math problems. Remember, learning is a journey, not a race. It's okay to make mistakes along the way, as long as you learn from them.

By following these tips, you'll be well-equipped to solve similar problems in the future. Keep up the great work and never stop learning!