Question

How many natural numbers less than 1000 have exactly three factors?

• A. 11
• B. 22
• C. 15
• D. 16

Answer 1

Answer: (A)

A number having exactly 3 factors must be the square of a prime number.
Prime numbers whose squares are less than 1000 are $2,3,5,7,11,13,17,19,23,29$, and 31 . The square of any prime number will have 3 factors.
$N=p^2$; the factors are $1,p$, and $p^2$.
$\therefore$ There are 11 such numbers which are less than 1000 .