Yes, 353 is a prime number. Its only factors are 1 and 353.
A number is prime if no smaller prime up to its square root divides it. The square root of 353 is about 18.79, 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 | 3 | No |
| 7 | 3 | No |
| 11 | 1 | No |
| 13 | 2 | No |
| 17 | 13 | No |
None of them divides 353 evenly, so 353 is prime.
| Number | Prime? |
|---|---|
| 349 | Yes |
| 350 | No, 2 × 5 × 5 × 7 |
| 351 | No, 3 × 3 × 3 × 13 |
| 352 | No, 2 × 2 × 2 × 2 × 2 × 11 |
| 354 | No, 2 × 3 × 59 |
| 355 | No, 5 × 71 |
| 356 | No, 2 × 2 × 89 |
| 357 | No, 3 × 7 × 17 |
Another number? Use the prime number checker for any value, or see the list of prime numbers.