Yes, 31 is a prime number. Its only factors are 1 and 31.
A number is prime if no smaller prime up to its square root divides it. The square root of 31 is about 5.57, so it is enough to test the primes 2, 3 and 5.
| Divide by | Remainder | Divides evenly? |
|---|---|---|
| 2 | 1 | No |
| 3 | 1 | No |
| 5 | 1 | No |
None of them divides 31 evenly, so 31 is prime.
| Number | Prime? |
|---|---|
| 27 | No, 3 × 3 × 3 |
| 28 | No, 2 × 2 × 7 |
| 29 | Yes |
| 30 | No, 2 × 3 × 5 |
| 32 | No, 2 × 2 × 2 × 2 × 2 |
| 33 | No, 3 × 11 |
| 34 | No, 2 × 17 |
| 35 | No, 5 × 7 |
More about 31: factors of 31 · 31 squared · square root of 31 · 31 in binary · 31 in Roman numerals.
Another number? Use the prime number checker for any value, or see the list of prime numbers.