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Consider the following statements: (I) All prime numbers are odd numbers. (Il) There are only five single digit prime numbers. (Ill) There are infinitely many prime numbers. (IV) A prime number has only two factors. Which of the above statements are true?

Consider the following statements: (I) All prime numbers are odd numbers. (Il) There are only five single digit prime numbers. (Ill) There are infinitely many prime numbers. (IV) A prime number has only two factors. Which of the above statements are true? Correct Answer <span style="">(III) and (IV)</span>

Explanation:

(I) All prime numbers are odd numbers.

2 is a prime number, which is an even number. Thus, false.

(Il) There are only five single-digit prime numbers.

2, 3, 5, 7 are the only single-digit prime numbers. Thus, false.

(Ill) There are infinitely many prime numbers.

There are infinitely many natural numbers. Thus, true.

(IV) A prime number has only two factors.

A prime number has only two factors, 1 and itself. Thus, true.

Hence, the correct option is (III) and (IV).

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