The number 33288
33288 is a composite number with 32 divisors. Its prime factorisation is × 3 × 19 × 73. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 73, 76, 114, 146, 152 … 33288.
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How to work it out
- 1
What is special about 33288: a Harshad number: divisible by its digit sum 24.
- 2
33288 is composite. Its prime factorisation is
- 3
The divisors add up to 88800; without 33288 itself that is 55512, so 33288 is abundant (55512 is more than 33288). Euler's totient φ(33288) = 10368 numbers up to 33288 share no factor with it.
- 4
The digits of 33288 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 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33288 = 2^{3} \times 3 \times 19 \times 73 \]33288 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 88800 |
| Euler totient φ(n) | 10368 |
| Square | 1108090944 |
| Cube | 36886131343872 |
| Square root | 182.449993 (= 2√8322) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.3288 × |
33288 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand two hundred and eighty-eight |
| Binary (base 2) | 1000001000001000 |
| Octal (base 8) | 101010 |
| Hexadecimal (base 16) | 8208 |
| Base 3 | 1200122220 |
| As time | 33288 seconds = 9 h 14 min 48 s |
Is 33288 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33288 ÷ 2 = 16644) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33288 ÷ 3 = 11096) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33288 ÷ 4 = 8322) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33288 ÷ 6 = 5548) | 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 (33288 ÷ 8 = 4161) | 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 8) | 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 (33288 ÷ 12 = 2774) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33288 a prime number?
No. 33288 = × 3 × 19 × 73, so it is divisible by 2.
What are the factors of 33288?
1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 73, 76, 114, 146, 152, 219, 228, 292, 438, 456, 584, 876, 1387, 1752, 2774, 4161, 5548, 8322, 11096, 16644, 33288.
What is 33288 in binary?
1000001000001000 (hexadecimal 8208, octal 101010).
What is the square root of 33288?
About 182.4500, exactly 2√8322.
Is 33288 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 33288?
33288 is a Harshad number: divisible by its digit sum 24.