The number 9585
9585 is a composite number with 16 divisors. Its prime factorisation is × 5 × 71. Divisors (16): 1, 3, 5, 9, 15, 27, 45, 71, 135, 213, 355, 639, 1065, 1917, 3195, 9585.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9585: a Harshad number: divisible by its digit sum 27.
- 2
9585 is composite. Its prime factorisation is
- 3
The divisors add up to 17280; without 9585 itself that is 7695, so 9585 is deficient (7695 is less than 9585). Euler's totient φ(9585) = 5040 numbers up to 9585 share no factor with it.
- 4
The digits of 9585 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9585 = 3^{3} \times 5 \times 71 \]9585 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 17280 |
| Euler totient φ(n) | 5040 |
| Square | 91872225 |
| Cube | 880595276625 |
| Square root | 97.903013 (= 3√1065) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 122 |
| Scientific notation | 9.585 × |
9585 in other forms
| Form | Value |
|---|---|
| In words | nine thousand five hundred and eighty-five |
| Binary (base 2) | 10010101110001 |
| Octal (base 8) | 22561 |
| Hexadecimal (base 16) | 2571 |
| Base 3 | 111011000 |
| As time | 9585 seconds = 2 h 39 min 45 s |
Is 9585 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 (9585 ÷ 3 = 3195) | 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 (9585 ÷ 5 = 1917) | 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 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9585 ÷ 9 = 1065) | 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 4) | 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 9585 a prime number?
No. 9585 = × 5 × 71, so it is divisible by 3.
What are the factors of 9585?
1, 3, 5, 9, 15, 27, 45, 71, 135, 213, 355, 639, 1065, 1917, 3195, 9585.
What is 9585 in binary?
10010101110001 (hexadecimal 2571, octal 22561).
What is the square root of 9585?
About 97.9030, exactly 3√1065.
Is 9585 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9585?
9585 is a Harshad number: divisible by its digit sum 27.