The number 33904
33904 is a composite number with 20 divisors. Its prime factorisation is × 13 × 163. Divisors (20): 1, 2, 4, 8, 13, 16, 26, 52, 104, 163, 208, 326, 652, 1304, 2119, 2608 … 33904.
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How to work it out
- 1
33904 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33904 is composite. Its prime factorisation is
- 3
The divisors add up to 71176; without 33904 itself that is 37272, so 33904 is abundant (37272 is more than 33904). Euler's totient φ(33904) = 15552 numbers up to 33904 share no factor with it.
- 4
The digits of 33904 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33904 = 2^{4} \times 13 \times 163 \]33904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 71176 |
| Euler totient φ(n) | 15552 |
| Square | 1149481216 |
| Cube | 38972011147264 |
| Square root | 184.130389 (= 4√2119) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.3904 × |
33904 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and four |
| Binary (base 2) | 1000010001110000 |
| Octal (base 8) | 102160 |
| Hexadecimal (base 16) | 8470 |
| Base 3 | 1201111201 |
| As time | 33904 seconds = 9 h 25 min 4 s |
Is 33904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33904 ÷ 2 = 16952) | 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 | Yes (33904 ÷ 4 = 8476) | 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 | No (remainder 4) | 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 | Yes (33904 ÷ 8 = 4238) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33904 a prime number?
No. 33904 = × 13 × 163, so it is divisible by 2.
What are the factors of 33904?
1, 2, 4, 8, 13, 16, 26, 52, 104, 163, 208, 326, 652, 1304, 2119, 2608, 4238, 8476, 16952, 33904.
What is 33904 in binary?
1000010001110000 (hexadecimal 8470, octal 102160).
What is the square root of 33904?
About 184.1304, exactly 4√2119.
Is 33904 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 33904?
It is a composite number with 20 divisors.