Yes, 409 is a prime number. Its only factors are 1 and 409.
A number is prime if no smaller prime up to its square root divides it. The square root of 409 is about 20.22, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17 and 19.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 1 | No |
| 5 | 4 | No |
| 7 | 3 | No |
| 11 | 2 | No |
| 13 | 6 | No |
| 17 | 1 | No |
| 19 | 10 | No |
None of them divides 409 evenly, so 409 is prime.
| Number | Prime? |
|---|---|
| 405 | No, 3 × 3 × 3 × 3 × 5 |
| 406 | No, 2 × 7 × 29 |
| 407 | No, 11 × 37 |
| 408 | No, 2 × 2 × 2 × 3 × 17 |
| 410 | No, 2 × 5 × 41 |
| 411 | No, 3 × 137 |
| 412 | No, 2 × 2 × 103 |
| 413 | No, 7 × 59 |
Another number? Use the prime number checker for any value, or see the list of prime numbers.