Finding Non-Prime Numbers And Their Units Digits

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Hey guys! Let's dive into a cool math problem. We're given a set of numbers and told that when written out, three of them are prime. Our mission? To figure out which numbers aren't prime and then find the sum of the digits in their ones place. It sounds fun, right? Let's get started!

Understanding Prime and Non-Prime Numbers

So, what exactly is a prime number? Well, a prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Think of it like this: if a number can only be divided evenly by 1 and itself, it's a prime number. The first few prime numbers are 2, 3, 5, 7, 11, and so on. They're the building blocks of all other numbers, kinda like the alphabet is for words! Non-prime numbers, on the other hand, are numbers that have more than two divisors. They're also called composite numbers. For example, 4 is a non-prime number because it can be divided by 1, 2, and 4. Similarly, 6 is also a non-prime since its divisors are 1, 2, 3, and 6. Knowing the difference is key to solving our problem.

Now, let's look at the numbers we're given. We've got 5002, 5003, 5005, 5007, 5008, 5009, 5010, and 5011. Our job is to figure out which of these are prime and which ones are not. We can do this by checking if the numbers are divisible by any numbers other than 1 and themselves. We don't have to check every number, though. Here's a handy trick: if a number is even (ends in 0, 2, 4, 6, or 8), it's divisible by 2. If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3. Also, any number ending in 0 or 5 is divisible by 5. These quick checks can save us a lot of time. Let's apply them to our list!

To be crystal clear, understanding prime and non-prime numbers is fundamental in number theory. Prime numbers are the atoms of numbers, and understanding their properties allows us to solve various mathematical problems, including this one.

Analyzing the Given Numbers

Let's go through the given numbers one by one, checking for primality. This is where our knowledge of prime numbers and divisibility rules comes into play! Remember, our goal is to identify the non-prime numbers and then find the sum of their units digits.

  • 5002: This number is even, meaning it is divisible by 2. Therefore, it's not prime. The units digit is 2.
  • 5003: Let's check this one. It's not divisible by 2 (it's odd), and the sum of its digits (5 + 0 + 0 + 3 = 8) isn't divisible by 3. However, we can also check for divisibility by 7, 11, 13, and so on, but 5003 happens to be a prime number. Remember, we are given that three of the numbers in the set are prime. We don't need to check too many divisors here.
  • 5005: This number ends in 5, meaning it's divisible by 5. So, it's not prime. The units digit is 5.
  • 5007: The sum of the digits (5 + 0 + 0 + 7 = 12) is divisible by 3, so 5007 is divisible by 3. Thus, it's not prime. The units digit is 7.
  • 5008: This number is even, thus divisible by 2, and therefore not prime. The units digit is 8.
  • 5009: Let's check it. It's not divisible by 2, 3, or 5. We can also check 7, 11, 13, etc. but this is a prime number.
  • 5010: This number is even, and also ends in 0, meaning it is divisible by both 2 and 5. This one's definitely not prime. The units digit is 0.
  • 5011: It's not divisible by 2, 3, or 5. This is a prime number.

So, after a little investigation, we've identified the non-prime numbers in our list. Now we just have to add up the units digits.

Calculating the Sum of Units Digits

Alright, we've done the hard work of figuring out which numbers are prime and which ones aren't. Now it's time for the easy part: finding the sum of the units digits of the non-prime numbers. From our analysis, the non-prime numbers are 5002, 5005, 5007, 5008, and 5010. Let's write down the units digits of these numbers: 2, 5, 7, 8, and 0. Now, let's add them up: 2 + 5 + 7 + 8 + 0 = 22! Simple as that.

The sum of the units digits of the non-prime numbers is 22. Easy peasy, right? The key here was to understand what a prime number is, apply divisibility rules, and carefully analyze each number in the list. Remember, in math problems, it is important to be systematic and organized. Take it step by step, and you'll get the right answer.

Also, it is crucial to recognize that the prime numbers in the list are 5003, 5009, and 5011, as indicated in the problem. Knowing this helped us focus our efforts on finding the non-prime numbers and their unit digits.

Putting it all Together

  • Identified Non-Prime Numbers: 5002, 5005, 5007, 5008, 5010
  • Units Digits: 2, 5, 7, 8, 0
  • Sum of Units Digits: 2 + 5 + 7 + 8 + 0 = 22

Therefore, the answer is A) 22!

Final Answer and Conclusion

So there you have it, guys! We've successfully navigated the world of prime and non-prime numbers to find the answer. We started with a set of numbers, identified the non-primes, and calculated the sum of their units digits. The final answer, as we found, is 22. This problem is a great example of how understanding basic math concepts can help you solve more complex problems. Keep practicing, and you'll become a math whiz in no time!

This exercise highlights the importance of understanding prime numbers and divisibility rules. These rules are valuable tools when working with whole numbers. By applying the rules consistently and methodically, anyone can effectively determine the primality of a number. Always double-check your work and ensure you understand the steps involved. Good job everyone!

Important Tip: Always double-check your work, and don't be afraid to break down the problem into smaller, more manageable steps. Math can be fun when you approach it with the right mindset! This entire problem is a great way to improve your number sense and your ability to work systematically. Keep up the excellent work, and always remember to enjoy the process of learning.