The number 37967
37967 is the 4013th prime number. Its only divisors are 1 and 37967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37967: the 4013th prime number.
- 2
37967 is prime, so its only factors are 1 and 37967. It is the 4013th prime; the next prime is 37987 and the one before is 37963.
- 3
The divisors add up to 37968; without 37967 itself that is 1, so 37967 is deficient (1 is less than 37967). Euler's totient φ(37967) = 37966 numbers up to 37967 share no factor with it.
- 4
The digits of 37967 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
37967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 37968 |
| Euler totient φ(n) | 37966 |
| Square | 1441493089 |
| Cube | 54729168110063 |
| Square root | 194.851225 |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.7967 × |
37967 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and sixty-seven |
| Binary (base 2) | 1001010001001111 |
| Octal (base 8) | 112117 |
| Hexadecimal (base 16) | 944F |
| Base 3 | 1221002012 |
| As time | 37967 seconds = 10 h 32 min 47 s |
Is 37967 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 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 6) | 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 5) | 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 6) | 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 37967 a prime number?
Yes. 37967 is divisible only by 1 and itself.
What are the factors of 37967?
1, 37967.
What is 37967 in binary?
1001010001001111 (hexadecimal 944F, octal 112117).
What is the square root of 37967?
About 194.8512.
Is 37967 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 37967?
37967 is the 4013th prime number.