Consider the following statements:
I. 91 is a prime number.
II. 1 is neither prime nor composite.
III. 2 is the only even prime number.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → II and III only
A prime number has exactly two factors, 1 and itself; a composite number has more than two factors.
I. 91 is a prime number. — Incorrect. 91 has factors other than 1 and itself: \(91=7\times13\), so its factors are 1, 7, 13 and 91 and it is composite.
II. 1 is neither prime nor composite. — Correct. 1 has only one factor (itself), so it fits neither definition.
III. 2 is the only even prime number. — Correct. 2 has exactly the two factors 1 and 2; every other even number also has 2 as a factor besides 1 and itself, so it has more than two factors.