Yes, 971 is a prime number. Its only factors are 1 and 971.
A number is prime if no smaller prime up to its square root divides it. The square root of 971 is about 31.16, so it is enough to test the primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 1 | No |
| 7 | 5 | No |
| 11 | 3 | No |
| 13 | 9 | No |
| 17 | 2 | No |
| 19 | 2 | No |
| 23 | 5 | No |
| 29 | 14 | No |
| 31 | 10 | No |
None of them divides 971 evenly, so 971 is prime.
| Number | Prime? |
|---|---|
| 901 | No, 17 × 53 |
| 911 | Yes |
| 919 | Yes |
| 949 | No, 13 × 73 |
| 991 | Yes |
| 997 | Yes |
| 1,000 | No, 2 × 2 × 2 × 5 × 5 × 5 |
| 1,001 | No, 7 × 11 × 13 |
Another number? Use the prime number checker for any value, or see the list of prime numbers.