The number 33504
33504 is a composite number with 24 divisors. Its prime factorisation is × 3 × 349. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 349, 698, 1047, 1396 … 33504.
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How to work it out
- 1
33504 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33504 is composite. Its prime factorisation is
- 3
The divisors add up to 88200; without 33504 itself that is 54696, so 33504 is abundant (54696 is more than 33504). Euler's totient φ(33504) = 11136 numbers up to 33504 share no factor with it.
- 4
The digits of 33504 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33504 = 2^{5} \times 3 \times 349 \]33504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 88200 |
| Euler totient φ(n) | 11136 |
| Square | 1122518016 |
| Cube | 37608843608064 |
| Square root | 183.040979 (= 4√2094) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3504 × |
33504 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand five hundred and four |
| Binary (base 2) | 1000001011100000 |
| Octal (base 8) | 101340 |
| Hexadecimal (base 16) | 82E0 |
| Base 3 | 1200221220 |
| As time | 33504 seconds = 9 h 18 min 24 s |
Is 33504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33504 ÷ 2 = 16752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33504 ÷ 3 = 11168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33504 ÷ 4 = 8376) | 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 (33504 ÷ 6 = 5584) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (33504 ÷ 8 = 4188) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33504 ÷ 12 = 2792) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33504 a prime number?
No. 33504 = × 3 × 349, so it is divisible by 2.
What are the factors of 33504?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 33504.
What is 33504 in binary?
1000001011100000 (hexadecimal 82E0, octal 101340).
What is the square root of 33504?
About 183.0410, exactly 4√2094.
Is 33504 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 33504?
It is a composite number with 24 divisors.