Yes, 701 is a prime number. Its only factors are 1 and 701.
A number is prime if no smaller prime up to its square root divides it. The square root of 701 is about 26.48, 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 | 1 | No |
| 11 | 8 | No |
| 13 | 12 | No |
| 17 | 4 | No |
| 19 | 17 | No |
| 23 | 11 | No |
None of them divides 701 evenly, so 701 is prime.
| Number | Prime? |
|---|---|
| 561 | No, 3 × 11 × 17 |
| 601 | Yes |
| 611 | No, 13 × 47 |
| 641 | Yes |
| 713 | No, 23 × 31 |
| 721 | No, 7 × 103 |
| 743 | Yes |
| 771 | No, 3 × 257 |
Another number? Use the prime number checker for any value, or see the list of prime numbers.