Number Classification: Is 17 Prime or Composite?

To determine whether $n = 17$ is a prime number, we will check if it has any divisors other than 1 and itself. A prime number has no divisors other than these two.

• Step 1: Calculate $\sqrt{17}$. Since $\sqrt{17} \approx 4.123$, we need to test divisibility by integers 2, 3, and 4.
• Step 2: Check divisibility by 2. Since 17 is odd, it is not divisible by 2.
• Step 3: Check divisibility by 3. The sum of the digits of 17 is $1 + 7 = 8$, which is not divisible by 3.
• Step 4: Check divisibility by 4. Half of 17 is not a whole number, thus it is not divisible by 4.

Since 17 is not divisible by any number other than 1 and itself, it satisfies the condition of being a prime number.

Therefore, the solution to the problem is Prime.