Yes, 307 is a prime number. Its only factors are 1 and 307.
A number is prime if no smaller prime up to its square root divides it. The square root of 307 is about 17.52, 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 | 2 | No |
| 7 | 6 | No |
| 11 | 10 | No |
| 13 | 8 | No |
| 17 | 1 | No |
None of them divides 307 evenly, so 307 is prime.
| Number | Prime? |
|---|---|
| 303 | No, 3 × 101 |
| 304 | No, 2 × 2 × 2 × 2 × 19 |
| 305 | No, 5 × 61 |
| 306 | No, 2 × 3 × 3 × 17 |
| 308 | No, 2 × 2 × 7 × 11 |
| 309 | No, 3 × 103 |
| 310 | No, 2 × 5 × 31 |
| 311 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.