The number 33997
33997 is the 3638th prime number. Its only divisors are 1 and 33997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33997: the 3638th prime number.
- 2
33997 is prime, so its only factors are 1 and 33997. It is the 3638th prime; the next prime is 34019 and the one before is 33967.
- 3
The divisors add up to 33998; without 33997 itself that is 1, so 33997 is deficient (1 is less than 33997). Euler's totient φ(33997) = 33996 numbers up to 33997 share no factor with it.
- 4
The digits of 33997 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 129 steps to reach 1.
33997 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 33998 |
| Euler totient φ(n) | 33996 |
| Square | 1155796009 |
| Cube | 39293596917973 |
| Square root | 184.382754 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3997 × |
33997 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and ninety-seven |
| Binary (base 2) | 1000010011001101 |
| Octal (base 8) | 102315 |
| Hexadecimal (base 16) | 84CD |
| Base 3 | 1201122011 |
| As time | 33997 seconds = 9 h 26 min 37 s |
Is 33997 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 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 5) | 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 4) | 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 7) | 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 33997 a prime number?
Yes. 33997 is divisible only by 1 and itself.
What are the factors of 33997?
1, 33997.
What is 33997 in binary?
1000010011001101 (hexadecimal 84CD, octal 102315).
What is the square root of 33997?
About 184.3828.
Is 33997 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 33997?
33997 is the 3638th prime number.