The number 585
585 is a palindrome: it reads 585 backwards too and a binary palindrome (1001001001). Its prime factorisation is × 5 × 13. Divisors (12): 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 585: a palindrome: it reads 585 backwards too; a binary palindrome (1001001001).
- 2
585 is composite. Its prime factorisation is
- 3
The divisors add up to 1092; without 585 itself that is 507, so 585 is deficient (507 is less than 585). Euler's totient φ(585) = 288 numbers up to 585 share no factor with it.
- 4
The digits of 585 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 585 = 3^{2} \times 5 \times 13 \]585 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1092 |
| Euler totient φ(n) | 288 |
| Square | 342225 |
| Cube | 200201625 |
| Square root | 24.186773 (= 3√65) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 5.85 × |
585 in other forms
| Form | Value |
|---|---|
| In words | five hundred and eighty-five |
| Roman numerals | DLXXXV |
| Binary (base 2) | 1001001001 |
| Octal (base 8) | 1111 |
| Hexadecimal (base 16) | 249 |
| Base 3 | 210200 |
| As time | 585 seconds = 9 min 45 s |
Is 585 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 (585 ÷ 3 = 195) | 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 (585 ÷ 5 = 117) | 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 4) | 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 (585 ÷ 9 = 65) | 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 2) | 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 585 a prime number?
No. 585 = × 5 × 13, so it is divisible by 3.
What are the factors of 585?
1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
What is 585 in binary?
1001001001 (hexadecimal 249, octal 1111).
What is the square root of 585?
About 24.1868, exactly 3√65.
What is 585 in Roman numerals?
DLXXXV.
Is 585 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 585?
585 is a palindrome: it reads 585 backwards too; a binary palindrome (1001001001).