Yes, 311 is a prime number. Its only factors are 1 and 311.
A number is prime if no smaller prime up to its square root divides it. The square root of 311 is about 17.64, so it is enough to test the primes 2, 3, 5, 7, 11, 13 and 17.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 1 | No |
| 7 | 3 | No |
| 11 | 3 | No |
| 13 | 12 | No |
| 17 | 5 | No |
None of them divides 311 evenly, so 311 is prime.
| Number | Prime? |
|---|---|
| 307 | Yes |
| 308 | No, 2 × 2 × 7 × 11 |
| 309 | No, 3 × 103 |
| 310 | No, 2 × 5 × 31 |
| 312 | No, 2 × 2 × 2 × 3 × 13 |
| 313 | Yes |
| 314 | No, 2 × 157 |
| 315 | No, 3 × 3 × 5 × 7 |
Another number? Use the prime number checker for any value, or see the list of prime numbers.