The number 33804
33804 is a composite number with 24 divisors. Its prime factorisation is × × 313. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 313, 626, 939, 1252 … 33804.
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How to work it out
- 1
What is special about 33804: a Harshad number: divisible by its digit sum 18.
- 2
33804 is composite. Its prime factorisation is
- 3
The divisors add up to 87920; without 33804 itself that is 54116, so 33804 is abundant (54116 is more than 33804). Euler's totient φ(33804) = 11232 numbers up to 33804 share no factor with it.
- 4
The digits of 33804 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33804 = 2^{2} \times 3^{3} \times 313 \]33804 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 87920 |
| Euler totient φ(n) | 11232 |
| Square | 1142710416 |
| Cube | 38628182902464 |
| Square root | 183.858641 (= 6√939) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 59 |
| Scientific notation | 3.3804 × |
33804 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand eight hundred and four |
| Binary (base 2) | 1000010000001100 |
| Octal (base 8) | 102014 |
| Hexadecimal (base 16) | 840C |
| Base 3 | 1201101000 |
| As time | 33804 seconds = 9 h 23 min 24 s |
Is 33804 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33804 ÷ 2 = 16902) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33804 ÷ 3 = 11268) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33804 ÷ 4 = 8451) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33804 ÷ 6 = 5634) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33804 ÷ 9 = 3756) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33804 ÷ 12 = 2817) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33804 a prime number?
No. 33804 = × × 313, so it is divisible by 2.
What are the factors of 33804?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 313, 626, 939, 1252, 1878, 2817, 3756, 5634, 8451, 11268, 16902, 33804.
What is 33804 in binary?
1000010000001100 (hexadecimal 840C, octal 102014).
What is the square root of 33804?
About 183.8586, exactly 6√939.
Is 33804 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 33804?
33804 is a Harshad number: divisible by its digit sum 18.