Prime Number Identification: Testing Numbers for Prime Properties

To determine which of the given numbers is a prime number, we will evaluate each one to check if it has any divisors other than 1 or itself.

Here are the steps:

• Step 1: Examine number 18:
  - 18 is divisible by 2 (as it is even) and also by 3 (since 1 + 8 = 9, which is divisible by 3). Therefore, 18 is not a prime number.
• Step 2: Examine number 21:
  - 21 is divisible by 3 (since 2 + 1 = 3, which is divisible by 3) and by 7 (as $21 \div 7 = 3$). Thus, 21 is not a prime number.
• Step 3: Examine number 16:
  - 16 is divisible by 2 (multiple times: 16, 8, 4, 2) and hence is not a prime number.
• Step 4: Examine number 19:
  - Check divisibility by 2: 19 is odd, not divisible by 2.
  - Check divisibility by 3: 1 + 9 = 10, not divisible by 3.
  - Check divisibility by 5: Does not end in 0 or 5.
  - Check divisibility by any prime numbers less than the square root of 19: None divides 19 evenly.
  As no number other than 1 and itself divides 19, it is a prime number.

Therefore, the solution is that $19$ is the prime number among the choices given.