Is 23 Prime?

Check if 23 is a prime number. A prime number is only divisible by 1 and itself.

Result: ✓ YES — 23 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 23 is prime, we need to verify that no number from 2 to √23 divides it evenly.

Step 2 Determine Testing Range

Since 23 is odd, we only need to check odd divisors.

We only need to test up to √23 ≈ 4.80, which rounds down to 4.

If 23 has a factor larger than √23, it must also have a corresponding factor smaller than √23.

Step 3 Test Odd Divisors

Testing: 3, 5, 7, ... up to 4

23 ÷ 3 = 7 remainder 2

None of these numbers divide 23 evenly.

Step 4 Conclusion

23 has no divisors between 2 and 4.

The only factors of 23 are 1 and 23 itself.

Therefore, 23 is a PRIME number!