The number 33967
33967 is the 3637th prime number. Its only divisors are 1 and 33967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33967: the 3637th prime number.
- 2
33967 is prime, so its only factors are 1 and 33967. It is the 3637th prime; the next prime is 33997 and the one before is 33961.
- 3
The divisors add up to 33968; without 33967 itself that is 1, so 33967 is deficient (1 is less than 33967). Euler's totient φ(33967) = 33966 numbers up to 33967 share no factor with it.
- 4
The digits of 33967 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
33967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 33968 |
| Euler totient φ(n) | 33966 |
| Square | 1153757089 |
| Cube | 39189667042063 |
| Square root | 184.301384 |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 111 |
| Scientific notation | 3.3967 × |
33967 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and sixty-seven |
| Binary (base 2) | 1000010010101111 |
| Octal (base 8) | 102257 |
| Hexadecimal (base 16) | 84AF |
| Base 3 | 1201121001 |
| As time | 33967 seconds = 9 h 26 min 7 s |
Is 33967 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 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 1) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33967 a prime number?
Yes. 33967 is divisible only by 1 and itself.
What are the factors of 33967?
1, 33967.
What is 33967 in binary?
1000010010101111 (hexadecimal 84AF, octal 102257).
What is the square root of 33967?
About 184.3014.
Is 33967 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 33967?
33967 is the 3637th prime number.