The number 37993
37993 is a twin prime (37991 and 37993 are both prime) and the 4016th prime number. Its only divisors are 1 and 37993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37993: a twin prime (37991 and 37993 are both prime); the 4016th prime number.
- 2
37993 is prime, so its only factors are 1 and 37993. It is the 4016th prime; the next prime is 37997 and the one before is 37991.
- 3
The divisors add up to 37994; without 37993 itself that is 1, so 37993 is deficient (1 is less than 37993). Euler's totient φ(37993) = 37992 numbers up to 37993 share no factor with it.
- 4
The digits of 37993 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 137 steps to reach 1.
37993 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 37994 |
| Euler totient φ(n) | 37992 |
| Square | 1443468049 |
| Cube | 54841681585657 |
| Square root | 194.917931 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.7993 × |
37993 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and ninety-three |
| Binary (base 2) | 1001010001101001 |
| Octal (base 8) | 112151 |
| Hexadecimal (base 16) | 9469 |
| Base 3 | 1221010011 |
| As time | 37993 seconds = 10 h 33 min 13 s |
Is 37993 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 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37993 a prime number?
Yes. 37993 is divisible only by 1 and itself.
What are the factors of 37993?
1, 37993.
What is 37993 in binary?
1001010001101001 (hexadecimal 9469, octal 112151).
What is the square root of 37993?
About 194.9179.
Is 37993 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 37993?
37993 is a twin prime (37991 and 37993 are both prime); the 4016th prime number.