Yes, 821 is a prime number. Its only factors are 1 and 821.
A number is prime if no smaller prime up to its square root divides it. The square root of 821 is about 28.65, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17, 19 and 23.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 1 | No |
| 7 | 2 | No |
| 11 | 7 | No |
| 13 | 2 | No |
| 17 | 5 | No |
| 19 | 4 | No |
| 23 | 16 | No |
None of them divides 821 evenly, so 821 is prime.
| Number | Prime? |
|---|---|
| 771 | No, 3 × 257 |
| 791 | No, 7 × 113 |
| 801 | No, 3 × 3 × 89 |
| 811 | Yes |
| 851 | No, 23 × 37 |
| 871 | No, 13 × 67 |
| 901 | No, 17 × 53 |
| 911 | Yes |
Another number? Use the prime number checker for any value, or see the list of prime numbers.