Yes, 313 is a prime number. Its only factors are 1 and 313.
A number is prime if no smaller prime up to its square root divides it. The square root of 313 is about 17.69, 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 | 1 | No |
| 5 | 3 | No |
| 7 | 5 | No |
| 11 | 5 | No |
| 13 | 1 | No |
| 17 | 7 | No |
None of them divides 313 evenly, so 313 is prime.
| Number | Prime? |
|---|---|
| 309 | No, 3 × 103 |
| 310 | No, 2 × 5 × 31 |
| 311 | Yes |
| 312 | No, 2 × 2 × 2 × 3 × 13 |
| 314 | No, 2 × 157 |
| 315 | No, 3 × 3 × 5 × 7 |
| 316 | No, 2 × 2 × 79 |
| 317 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.