Prime Number Identification: Testing for Prime Properties

To solve this problem, we'll identify which of the given numbers is a prime number:

• Step 1: Define a prime number as a positive integer greater than 1 that has no divisors other than 1 and itself.
• Step 2: Examine each number and list its divisors.

Now, let's work through each step:

Step 1: Consider the numbers given: $9$, $11$, $8$, and $4$.

Step 2:

• $9$ has divisors $1, 3, 9$. Since it has more than two divisors, it is not a prime number.
• $11$ has divisors $1, 11$. Since it has exactly two divisors, it is a prime number.
• $8$ has divisors $1, 2, 4, 8$. Since it has more than two divisors, it is not a prime number.
• $4$ has divisors $1, 2, 4$. Since it has more than two divisors, it is not a prime number.

Therefore, the number that is a prime number is $11$.