Question

If $p$ is a prime number, find the number of factors of a number $p^3$.

• A. One
• B. Two
• C. Three
• D. Four

Answer 1

Answer: (D)

Four

The answer must be true for any value of $p$, so plug in an easy (prime) number for $p$, such as $2$.

The factors of $2^3=8$ are $1,2,4$, and $8$, so answer D is correct.

In general, since $p$ is prime, the only numbers that go into $p^3$ without a remainder are $1,p,p^2$, and $p^3$.