The product of two prime numbers is(1 point)
Responses
neither prime nor composite.
neither prime nor composite.
both prime and composite.
both prime and composite.
composite.
composite.
prime.
The correct answer is "composite."
To determine whether the product of two numbers is prime or composite, we need to understand the definitions of prime and composite numbers.
Prime numbers are numbers greater than 1 that have only two distinct factors: 1 and the number itself. For example, 2, 3, 5, and 7 are prime numbers.
Composite numbers, on the other hand, have factors other than 1 and the number itself. In other words, they are divisible by at least one number other than 1 and itself. For example, 4, 6, 8, and 9 are composite numbers.
Now, when we take the product of two prime numbers, we are multiplying two numbers that have only two factors each.
Since the factors of a number are preserved when we multiply, the product of two prime numbers will have more than two factors. In fact, it will have all the factors of each prime number multiplied together.
Therefore, the product of two prime numbers will always be a composite number.