Number Classification: Identify the Type of Number 11

What type of number is the number n shown below?

$n=11$

To solve this problem, we'll follow these steps:

• Step 1: Verify if the number $n = 11$ is divisible by any numbers other than 1 and itself.
• Step 2: Based on the result of the divisibility test, determine the type of number.

Now, let's work through each step:

Step 1: Check divisibility.
The number 11 is greater than 2, so we check divisibility by smaller primes up to $\sqrt{11} \approx 3.3$. The prime numbers less than or equal to 3 are 2 and 3.

- **Divisibility by 2:** 11 is an odd number, hence not divisible by 2.
- **Divisibility by 3:** Sum of digits of 11 is $1 + 1 = 2$, which is not divisible by 3.

Step 2: Conclusion based on divisibility.
Since 11 is not divisible by any other numbers except 1 and 11 itself, it does not have any divisors other than 1 and itself. Therefore, 11 is a prime number.

Hence, the solution to the problem is $n = 11$ is Prime.