CAT 2023 Slot 2 QA Question 5: The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

Question

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

Accepted Answer

A number with exactly two factors other than 1 and itself has exactly four positive factors.

Such a number must be of the form $p^{3}$ or $p 	imes q$, where $p$ and $q$ are distinct primes.

For $p^3

For $pq 
$p = 2$ gives $q = 3, 5, 7, 11, 13, 17, 19, 23$: 8 numbers
$p = 3$ gives $q = 5, 7, 11,