Question

If n= 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

• A. Two
• B. Three
• C. Four
• D. Six
• E. Eight

Answer 1

The correct option is C Four

$n=4p$

Factors of $4p$ are

$1$ which is a factor of every number

$2$ as $4p$ is divisible by $2$

$4$ as $4p$ is divisible by $4$

$p$ as $4p$ is divisible by $p$

$2p$ as $4p$ is divisible by $2p$

$4p$ as $4p$ is divisible by $4p$

Now $p$ is prime $>2$ therefore $p$ is an odd integer.

So the even divisors of $4p$ are $2,4,2p,4p$

We have four even divisors.

Option $C$ is correct.