Yes, 317 is a prime number. Its only factors are 1 and 317.
A number is prime if no smaller prime up to its square root divides it. The square root of 317 is about 17.80, 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 | 2 | No |
| 7 | 2 | No |
| 11 | 9 | No |
| 13 | 5 | No |
| 17 | 11 | No |
None of them divides 317 evenly, so 317 is prime.
| Number | Prime? |
|---|---|
| 313 | Yes |
| 314 | No, 2 × 157 |
| 315 | No, 3 × 3 × 5 × 7 |
| 316 | No, 2 × 2 × 79 |
| 318 | No, 2 × 3 × 53 |
| 319 | No, 11 × 29 |
| 320 | No, 2 × 2 × 2 × 2 × 2 × 2 × 5 |
| 321 | No, 3 × 107 |
Another number? Use the prime number checker for any value, or see the list of prime numbers.