The number 10585
10585 is a triangular number: 1 + 2 + … + 145 = 10585. Its prime factorisation is 5 × 29 × 73. Divisors (8): 1, 5, 29, 73, 145, 365, 2117, 10585.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10585: a triangular number: 1 + 2 + … + 145 = 10585.
- 2
10585 is composite. Its prime factorisation is
- 3
The divisors add up to 13320; without 10585 itself that is 2735, so 10585 is deficient (2735 is less than 10585). Euler's totient φ(10585) = 8064 numbers up to 10585 share no factor with it.
- 4
The digits of 10585 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 148 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10585 = 5 \times 29 \times 73 \]
10585 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 13320 |
| Euler totient φ(n) | 8064 |
| Square | 112042225 |
| Cube | 1185966951625 |
| Square root | 102.883429 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 148 |
| Scientific notation | 1.0585 × |
10585 in other forms
| Form | Value |
|---|---|
| In words | ten thousand five hundred and eighty-five |
| Binary (base 2) | 10100101011001 |
| Octal (base 8) | 24531 |
| Hexadecimal (base 16) | 2959 |
| Base 3 | 112112001 |
| As time | 10585 seconds = 2 h 56 min 25 s |
Is 10585 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 | No (remainder 1) | 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 (10585 ÷ 5 = 2117) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 1) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10585 a prime number?
No. 10585 = 5 × 29 × 73, so it is divisible by 5.
What are the factors of 10585?
1, 5, 29, 73, 145, 365, 2117, 10585.
What is 10585 in binary?
10100101011001 (hexadecimal 2959, octal 24531).
What is the square root of 10585?
About 102.8834.
Is 10585 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 10585?
10585 is a triangular number: 1 + 2 + … + 145 = 10585.