The number 32385
32385 is a triangular number: 1 + 2 + … + 254 = 32385. Its prime factorisation is 3 × 5 × 17 × 127. Divisors (16): 1, 3, 5, 15, 17, 51, 85, 127, 255, 381, 635, 1905, 2159, 6477, 10795, 32385.
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How to work it out
- 1
What is special about 32385: a triangular number: 1 + 2 + … + 254 = 32385.
- 2
32385 is composite. Its prime factorisation is
- 3
The divisors add up to 55296; without 32385 itself that is 22911, so 32385 is deficient (22911 is less than 32385). Euler's totient φ(32385) = 16128 numbers up to 32385 share no factor with it.
- 4
The digits of 32385 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32385 = 3 \times 5 \times 17 \times 127 \]
32385 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 55296 |
| Euler totient φ(n) | 16128 |
| Square | 1048788225 |
| Cube | 33965006666625 |
| Square root | 179.958329 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.2385 × |
32385 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand three hundred and eighty-five |
| Binary (base 2) | 111111010000001 |
| Octal (base 8) | 77201 |
| Hexadecimal (base 16) | 7E81 |
| Base 3 | 1122102110 |
| As time | 32385 seconds = 8 h 59 min 45 s |
Is 32385 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32385 ÷ 3 = 10795) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32385 ÷ 5 = 6477) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 | No (remainder 1) | 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 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32385 a prime number?
No. 32385 = 3 × 5 × 17 × 127, so it is divisible by 3.
What are the factors of 32385?
1, 3, 5, 15, 17, 51, 85, 127, 255, 381, 635, 1905, 2159, 6477, 10795, 32385.
What is 32385 in binary?
111111010000001 (hexadecimal 7E81, octal 77201).
What is the square root of 32385?
About 179.9583.
Is 32385 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 32385?
32385 is a triangular number: 1 + 2 + … + 254 = 32385.