Classify zero (0) as prime or composite.(1 point)
Responses
composite
composite
prime
prime
both prime and composite
both prime and composite
neither prime nor composite
neither prime nor composite
Zero (0) is neither prime nor composite.
To understand why, let's go through the definitions of prime and composite numbers:
1. Prime Number: A prime number is a positive integer greater than 1 that has exactly two distinct positive divisors: 1 and itself.
2. Composite Number: A composite number is a positive integer greater than 1 that has more than two distinct positive divisors, meaning it can be divided evenly by at least one number other than 1 and itself.
Given these definitions, we can analyze the number 0:
- For 0 to be prime, it should have exactly two distinct positive divisors (1 and itself). However, since 0 cannot be divided by any positive integer other than itself (0 divided by any nonzero number is undefined), it fails the requirement of having exactly two distinct positive divisors. Therefore, 0 is not a prime number.
- For 0 to be composite, it should have more than two distinct positive divisors. However, as explained earlier, 0 cannot be divided by any positive integer other than itself, which means it does not have more than two distinct positive divisors. Therefore, 0 is not a composite number either.
Hence, we conclude that 0 is neither prime nor composite.