Yes, 1,801 is a prime number. Its only factors are 1 and 1,801.
A number is prime if no smaller prime up to its square root divides it. The square root of 1,801 is about 42.44, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 and 41.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 1 | No |
| 5 | 1 | No |
| 7 | 2 | No |
| 11 | 8 | No |
| 13 | 7 | No |
| 17 | 16 | No |
| 19 | 15 | No |
| 23 | 7 | No |
| 29 | 3 | No |
| 31 | 3 | No |
| 37 | 25 | No |
| 41 | 38 | No |
None of them divides 1,801 evenly, so 1,801 is prime.
| Number | Prime? |
|---|---|
| 1,459 | Yes |
| 1,501 | No, 19 × 79 |
| 1,601 | Yes |
| 1,729 | No, 7 × 13 × 19 |
| 1,901 | Yes |
| 1,999 | Yes |
| 2,001 | No, 3 × 23 × 29 |
| 2,003 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.