The number 8385
8385 is a triangular number: 1 + 2 + … + 129 = 8385 and a binary palindrome (10000011000001). Its prime factorisation is 3 × 5 × 13 × 43. Divisors (16): 1, 3, 5, 13, 15, 39, 43, 65, 129, 195, 215, 559, 645, 1677, 2795, 8385.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8385: a triangular number: 1 + 2 + … + 129 = 8385; a binary palindrome (10000011000001).
- 2
8385 is composite. Its prime factorisation is
- 3
The divisors add up to 14784; without 8385 itself that is 6399, so 8385 is deficient (6399 is less than 8385). Euler's totient φ(8385) = 4032 numbers up to 8385 share no factor with it.
- 4
The digits of 8385 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 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8385 = 3 \times 5 \times 13 \times 43 \]
8385 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 14784 |
| Euler totient φ(n) | 4032 |
| Square | 70308225 |
| Cube | 589534466625 |
| Square root | 91.569646 |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 65 |
| Scientific notation | 8.385 × |
8385 in other forms
| Form | Value |
|---|---|
| In words | eight thousand three hundred and eighty-five |
| Binary (base 2) | 10000011000001 |
| Octal (base 8) | 20301 |
| Hexadecimal (base 16) | 20C1 |
| Base 3 | 102111120 |
| As time | 8385 seconds = 2 h 19 min 45 s |
Is 8385 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 (8385 ÷ 3 = 2795) | 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 (8385 ÷ 5 = 1677) | 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 6) | 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 6) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8385 a prime number?
No. 8385 = 3 × 5 × 13 × 43, so it is divisible by 3.
What are the factors of 8385?
1, 3, 5, 13, 15, 39, 43, 65, 129, 195, 215, 559, 645, 1677, 2795, 8385.
What is 8385 in binary?
10000011000001 (hexadecimal 20C1, octal 20301).
What is the square root of 8385?
About 91.5696.
Is 8385 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 8385?
8385 is a triangular number: 1 + 2 + … + 129 = 8385; a binary palindrome (10000011000001).