Is 11 Prime?

Check if 11 is a prime number. A prime number is only divisible by 1 and itself.

Result: ✓ YES — 11 is a prime number

Step-by-Step Solution

Step 1 What is a Prime Number?

A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.

To check if 11 is prime, we need to verify that no number from 2 to √11 divides it evenly.

Step 2 Determine Testing Range

Since 11 is odd, we only need to check odd divisors.

We only need to test up to √11 ≈ 3.32, which rounds down to 3.

If 11 has a factor larger than √11, it must also have a corresponding factor smaller than √11.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 3

11 ÷ 3 = 3 remainder 2

None of these numbers divide 11 evenly.

Step 4 Conclusion

11 has no divisors between 2 and 3.

The only factors of 11 are 1 and 11 itself.

Therefore, 11 is a PRIME number!