The number 33024
33024 is a composite number with 36 divisors. Its prime factorisation is × 3 × 43. Divisors (36): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 43, 48, 64, 86, 96, 128 … 33024.
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How to work it out
- 1
What is special about 33024: a Harshad number: divisible by its digit sum 12.
- 2
33024 is composite. Its prime factorisation is
- 3
The divisors add up to 89936; without 33024 itself that is 56912, so 33024 is abundant (56912 is more than 33024). Euler's totient φ(33024) = 10752 numbers up to 33024 share no factor with it.
- 4
The digits of 33024 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33024 = 2^{8} \times 3 \times 43 \]33024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 89936 |
| Euler totient φ(n) | 10752 |
| Square | 1090584576 |
| Cube | 36015465037824 |
| Square root | 181.725067 (= 16√129) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3024 × |
33024 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and twenty-four |
| Binary (base 2) | 1000000100000000 |
| Octal (base 8) | 100400 |
| Hexadecimal (base 16) | 8100 |
| Base 3 | 1200022010 |
| As time | 33024 seconds = 9 h 10 min 24 s |
Is 33024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33024 ÷ 2 = 16512) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33024 ÷ 3 = 11008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33024 ÷ 4 = 8256) | 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 (33024 ÷ 6 = 5504) | 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 | Yes (33024 ÷ 8 = 4128) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (33024 ÷ 12 = 2752) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33024 a prime number?
No. 33024 = × 3 × 43, so it is divisible by 2.
What are the factors of 33024?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 43, 48, 64, 86, 96, 128, 129, 172, 192, 256, 258, 344, 384, 516, 688, 768, 1032, 1376, 2064, 2752, 4128, 5504, 8256, 11008, 16512, 33024.
What is 33024 in binary?
1000000100000000 (hexadecimal 8100, octal 100400).
What is the square root of 33024?
About 181.7251, exactly 16√129.
Is 33024 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 33024?
33024 is a Harshad number: divisible by its digit sum 12.