The number 37991
37991 is a twin prime (37991 and 37993 are both prime) and the 4015th prime number. Its only divisors are 1 and 37991.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37991: a twin prime (37991 and 37993 are both prime); the 4015th prime number.
- 2
37991 is prime, so its only factors are 1 and 37991. It is the 4015th prime; the next prime is 37993 and the one before is 37987.
- 3
The divisors add up to 37992; without 37991 itself that is 1, so 37991 is deficient (1 is less than 37991). Euler's totient φ(37991) = 37990 numbers up to 37991 share no factor with it.
- 4
The digits of 37991 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 186 steps to reach 1.
37991 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 37992 |
| Euler totient φ(n) | 37990 |
| Square | 1443316081 |
| Cube | 54833021233271 |
| Square root | 194.912801 |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 186 |
| Scientific notation | 3.7991 × |
37991 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and ninety-one |
| Binary (base 2) | 1001010001100111 |
| Octal (base 8) | 112147 |
| Hexadecimal (base 16) | 9467 |
| Base 3 | 1221010002 |
| As time | 37991 seconds = 10 h 33 min 11 s |
Is 37991 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37991 a prime number?
Yes. 37991 is divisible only by 1 and itself.
What are the factors of 37991?
1, 37991.
What is 37991 in binary?
1001010001100111 (hexadecimal 9467, octal 112147).
What is the square root of 37991?
About 194.9128.
Is 37991 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 37991?
37991 is a twin prime (37991 and 37993 are both prime); the 4015th prime number.