Yes, 223 is a prime number. Its only factors are 1 and 223.
A number is prime if no smaller prime up to its square root divides it. The square root of 223 is about 14.93, so it is enough to test the primes 2, 3, 5, 7, 11 and 13.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 1 | No |
| 5 | 3 | No |
| 7 | 6 | No |
| 11 | 3 | No |
| 13 | 2 | No |
None of them divides 223 evenly, so 223 is prime.
| Number | Prime? |
|---|---|
| 219 | No, 3 × 73 |
| 220 | No, 2 × 2 × 5 × 11 |
| 221 | No, 13 × 17 |
| 222 | No, 2 × 3 × 37 |
| 224 | No, 2 × 2 × 2 × 2 × 2 × 7 |
| 225 | No, 3 × 3 × 5 × 5 |
| 226 | No, 2 × 113 |
| 227 | Yes |
More about 223: 223 in binary.
Another number? Use the prime number checker for any value, or see the list of prime numbers.