Greta says the product of two prime numbers must also be prime. Joan disagreed. Who is correct?
The product of two prime numbers is NEVER a prime number becouse that it is a product and therefore has factors.
To determine who is correct - Greta or Joan - we need to understand the concept of prime numbers.
A prime number is a number greater than 1 that only has two positive divisors: 1 and itself. For example, 2, 3, 5, and 7 are prime numbers because they are only divisible by 1 and the number itself.
Now, suppose we have two prime numbers, let's say p and q. Greta is claiming that their product (p * q) must also be prime. Joan, on the other hand, disagrees with this statement.
To determine who is correct, we can consider a counterexample. A counterexample is a specific example that contradicts a general statement. In this case, if we find just one instance where the product of two prime numbers is not prime, Joan's claim would be proven correct.
Let's take an example: p = 2 and q = 3. Both 2 and 3 are prime numbers. If we calculate their product (2 * 3), we get 6. However, 6 is not prime because it has divisors other than 1 and itself (2 and 3).
Therefore, by finding this counterexample, we have shown that Greta's claim is incorrect, and Joan is correct. The product of two prime numbers does not necessarily have to be prime.