Yes, 167 is a prime number. Its only factors are 1 and 167.
A number is prime if no smaller prime up to its square root divides it. The square root of 167 is about 12.92, so it is enough to test the primes 2, 3, 5, 7 and 11.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 2 | No |
| 5 | 2 | No |
| 7 | 6 | No |
| 11 | 2 | No |
None of them divides 167 evenly, so 167 is prime.
| Number | Prime? |
|---|---|
| 163 | Yes |
| 164 | No, 2 × 2 × 41 |
| 165 | No, 3 × 5 × 11 |
| 166 | No, 2 × 83 |
| 168 | No, 2 × 2 × 2 × 3 × 7 |
| 169 | No, 13 × 13 |
| 170 | No, 2 × 5 × 17 |
| 171 | No, 3 × 3 × 19 |
More about 167: factors of 167 · square root of 167 · 167 in binary.
Another number? Use the prime number checker for any value, or see the list of prime numbers.