Question

Which of the following have exactly three factors?

• A. 13
• B. 25
• C. 125
• D. 21

Answer 1

The correct option is B

25

Numbers which are the squares of prime numbers have exactly three factors

They are: 1, the square root of the number and the number itself.

$25=5\times 5$ (Here 5 is the prime number)

Hence 25 has exactly three factors

13 is a prime number, and has only two factors.
$125=5\times 5\times 5$, and thus has exactly 3+1 = 4 factors.
Also, $21=3\times 7$ and thus has (1+1)(1+1)=4 factors in all.