The number 37997
37997 is the 4017th prime number. Its only divisors are 1 and 37997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37997: the 4017th prime number.
- 2
37997 is prime, so its only factors are 1 and 37997. It is the 4017th prime; the next prime is 38011 and the one before is 37993.
- 3
The divisors add up to 37998; without 37997 itself that is 1, so 37997 is deficient (1 is less than 37997). Euler's totient φ(37997) = 37996 numbers up to 37997 share no factor with it.
- 4
The digits of 37997 add up to 35, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 106 steps to reach 1.
37997 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 37998 |
| Euler totient φ(n) | 37996 |
| Square | 1443772009 |
| Cube | 54859005025973 |
| Square root | 194.928192 |
| Digit sum / digital root | 35 / 8 |
| Collatz steps to 1 | 106 |
| Scientific notation | 3.7997 × |
37997 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and ninety-seven |
| Binary (base 2) | 1001010001101101 |
| Octal (base 8) | 112155 |
| Hexadecimal (base 16) | 946D |
| Base 3 | 1221010022 |
| As time | 37997 seconds = 10 h 33 min 17 s |
Is 37997 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 1) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37997 a prime number?
Yes. 37997 is divisible only by 1 and itself.
What are the factors of 37997?
1, 37997.
What is 37997 in binary?
1001010001101101 (hexadecimal 946D, octal 112155).
What is the square root of 37997?
About 194.9282.
Is 37997 divisible by 3?
No. Its digits add up to 35, which is not a multiple of 3.
What is special about the number 37997?
37997 is the 4017th prime number.