The number 33792
33792 is a composite number with 44 divisors. Its prime factorisation is × 3 × 11. Divisors (44): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64 … 33792.
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How to work it out
- 1
What is special about 33792: a Harshad number: divisible by its digit sum 24.
- 2
33792 is composite. Its prime factorisation is
- 3
The divisors add up to 98256; without 33792 itself that is 64464, so 33792 is abundant (64464 is more than 33792). Euler's totient φ(33792) = 10240 numbers up to 33792 share no factor with it.
- 4
The digits of 33792 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33792 = 2^{10} \times 3 \times 11 \]33792 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 44 |
| Sum of divisors | 98256 |
| Euler totient φ(n) | 10240 |
| Square | 1141899264 |
| Cube | 38587059929088 |
| Square root | 183.826005 (= 32√33) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.3792 × |
33792 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand seven hundred and ninety-two |
| Binary (base 2) | 1000010000000000 |
| Octal (base 8) | 102000 |
| Hexadecimal (base 16) | 8400 |
| Base 3 | 1201100120 |
| As time | 33792 seconds = 9 h 23 min 12 s |
Is 33792 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33792 ÷ 2 = 16896) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33792 ÷ 3 = 11264) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33792 ÷ 4 = 8448) | 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 | Yes (33792 ÷ 6 = 5632) | 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 (33792 ÷ 8 = 4224) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (33792 ÷ 11 = 3072) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33792 ÷ 12 = 2816) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33792 a prime number?
No. 33792 = × 3 × 11, so it is divisible by 2.
What are the factors of 33792?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 256, 264, 352, 384, 512, 528, 704, 768, 1024, 1056, 1408, 1536, 2112, 2816, 3072, 4224, 5632, 8448, 11264, 16896, 33792.
What is 33792 in binary?
1000010000000000 (hexadecimal 8400, octal 102000).
What is the square root of 33792?
About 183.8260, exactly 32√33.
Is 33792 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 33792?
33792 is a Harshad number: divisible by its digit sum 24.