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List the prime numbers between 20 and 40 . Round off each of these prime numbers to the nearest 10 . Add all these prime numbers together. Is this total numbe prime number?

Ask by Chan Huang. in South Africa
Feb 03,2025

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Answer

The prime numbers between 20 and 40 are 23, 29, 31, and 37. When rounded to the nearest 10, they become 20, 30, 30, and 40. Adding them together gives 120. However, 120 is not a prime number because it has multiple divisors.

Solution

Sure, let's go through each step of your request: ### 1. **List of Prime Numbers Between 20 and 40** Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers between 20 and 40 are: - **23** - **29** - **31** - **37** ### 2. **Rounding Each Prime Number to the Nearest 10** - **23** → **20** (Since 23 is closer to 20 than to 30) - **29** → **30** (Since 29 is closer to 30 than to 20) - **31** → **30** (Since 31 is closer to 30 than to 40) - **37** → **40** (Since 37 is closer to 40 than to 30) ### 3. **Adding the Rounded Numbers Together** \[ 20 + 30 + 30 + 40 = 120 \] ### 4. **Is the Total Number (120) a Prime Number?** No, **120** is **not** a prime number. **Reason:** A prime number has exactly two distinct positive divisors: 1 and itself. 120 has multiple divisors, including: - 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. Since 120 has more than two divisors, it is a composite number, not a prime number. ### **Summary** - **Prime Numbers Between 20 and 40:** 23, 29, 31, 37 - **Rounded to Nearest 10:** 20, 30, 30, 40 - **Total Sum:** 120 - **Is 120 Prime?** No

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The prime numbers between 20 and 40 are 23, 29, 31, and 37. Rounding them to the nearest ten gives us 20, 30, 30, and 40, respectively. When we add all the prime numbers together (23 + 29 + 31 + 37), we get a total of 120. Unfortunately, 120 is not a prime number, as it can be divided by 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and of course itself! Prime numbers have fascinated mathematicians for centuries. As unbreakable building blocks of mathematics, they appear in patterns that seem random yet follow intriguing rules. Their unique properties inspire a wealth of research, from cryptography to computer algorithms, making them crucial in today’s digital age! If you ever find yourself pondering prime numbers, consider diving into their applications in real life. For instance, cryptography, the backbone of online security, relies heavily on prime numbers to keep your information safe. Large primes are particularly valuable for creating digital keys that secure everything from emails to online transactions. So the next time you buy something online, remember the prime numbers working behind the scenes!

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