Is 31 Prime?

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

To check if 31 is prime, we need to verify that no number from 2 to √31 divides it evenly.

Since 31 is odd, we only need to check odd divisors.

We only need to test up to √31 ≈ 5.57, which rounds down to 5.

If 31 has a factor larger than √31, it must also have a corresponding factor smaller than √31.

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

None of these numbers divide 31 evenly.

31 has no divisors between 2 and 5.

The only factors of 31 are 1 and 31 itself.

Therefore, 31 is a PRIME number!