Number Theory Practice: Identifying Prime Numbers

To determine which number is a prime number, we will check each choice for primality based on whether it has divisors other than 1 and itself:

• Check $16$: This number is even and divisible by 2, hence not prime.
• Check $17$: Testing divisibility by integers up to the square root of 17 (roughly 4.1), we find no divisors other than 1 and $17$ itself. Therefore, $17$ is prime.
• Check $18$: This number is even and divisible by 2, hence not prime.
• Check $14$: This number is also even and divisible by 2, hence not prime.

Given these observations, the only prime number among the choices is $17$.