Which statement correctly defines a prime number?

Which statement correctly defines a prime number?

• A. A number that is greater than 1 has no positive divisors.
• B. A number that can only be divided by itself and 1.
• C. A natural number with many factors.
• D. A number that is divisible by all integers.

Answer: (B)

A prime number is a natural number greater than 1 that has exactly two positive divisors: 1 and the number itself. This means it can be divided evenly only by 1 and by itself. That’s why the statement describing a prime as something that can only be divided by itself and 1 is the correct definition. The other ideas don’t fit: a number greater than 1 does have positive divisors (at least itself), so that claim is false. A natural number with many factors describes a composite number, not a prime. And a number divisible by all integers isn’t possible for any natural number (except, issue aside, numbers like 0—but 0 isn’t a natural number).

A prime number is a natural number greater than 1 that has exactly two positive divisors: 1 and the number itself. This means it can be divided evenly only by 1 and by itself.

That’s why the statement describing a prime as something that can only be divided by itself and 1 is the correct definition. The other ideas don’t fit: a number greater than 1 does have positive divisors (at least itself), so that claim is false. A natural number with many factors describes a composite number, not a prime. And a number divisible by all integers isn’t possible for any natural number (except, issue aside, numbers like 0—but 0 isn’t a natural number).