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1.1 Which of these set of numbers are prime numbers? A) \( 1,2,5 \) B) \( 2,4,6 \) C) \( 2,3,5 \) D) \( 5,7,9 \)

Ask by Mccarthy Cox. in South Africa
Mar 05,2025

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Tutor-Verified Answer

Answer

Option C (\(2, 3, 5\)) consists entirely of prime numbers.

Solution

Let's analyze each option step by step. 1. **Option A: \(1, 2, 5\)** - \(1\) is not a prime number (by definition, primes are greater than 1). - \(2\) is prime. - \(5\) is prime. - Since \(1\) is not prime, this set is not entirely composed of prime numbers. 2. **Option B: \(2, 4, 6\)** - \(2\) is prime. - \(4\) is not prime because \(4 = 2 \times 2\). - \(6\) is not prime because \(6 = 2 \times 3\). - This set contains non-prime numbers. 3. **Option C: \(2, 3, 5\)** - \(2\) is prime. - \(3\) is prime. - \(5\) is prime. - All numbers in this set are prime numbers. 4. **Option D: \(5, 7, 9\)** - \(5\) is prime. - \(7\) is prime. - \(9\) is not prime because \(9 = 3 \times 3\). - This set contains a non-prime number. **Conclusion:** The set that contains only prime numbers is Option C: \(2, 3, 5\).

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Beyond the Answer

To identify prime numbers, remember that a prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The only even prime number is 2, while all other prime numbers are odd. Based on this knowledge, the only set of numbers among the options that contains all prime numbers is C) \( 2,3,5 \). It’s pretty fun to explore the world of primes—they pop up in all sorts of places, like cryptography and patterns in nature! For instance, the distribution of prime numbers ties in closely with the famous Riemann Hypothesis, which attempts to understand the prime number distribution better. So, get ready to dive into a mathematical mystery!

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