The number 765
765 is a binary palindrome (1011111101). Its prime factorisation is × 5 × 17. Divisors (12): 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 765: a binary palindrome (1011111101).
- 2
765 is composite. Its prime factorisation is
- 3
The divisors add up to 1404; without 765 itself that is 639, so 765 is deficient (639 is less than 765). Euler's totient φ(765) = 384 numbers up to 765 share no factor with it.
- 4
The digits of 765 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 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 765 = 3^{2} \times 5 \times 17 \]765 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1404 |
| Euler totient φ(n) | 384 |
| Square | 585225 |
| Cube | 447697125 |
| Square root | 27.658633 (= 3√85) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 46 |
| Scientific notation | 7.65 × |
765 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and sixty-five |
| Roman numerals | DCCLXV |
| Binary (base 2) | 1011111101 |
| Octal (base 8) | 1375 |
| Hexadecimal (base 16) | 2FD |
| Base 3 | 1001100 |
| As time | 765 seconds = 12 min 45 s |
Is 765 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 (765 ÷ 3 = 255) | 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 (765 ÷ 5 = 153) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (765 ÷ 9 = 85) | 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 6) | 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 765 a prime number?
No. 765 = × 5 × 17, so it is divisible by 3.
What are the factors of 765?
1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765.
What is 765 in binary?
1011111101 (hexadecimal 2FD, octal 1375).
What is the square root of 765?
About 27.6586, exactly 3√85.
What is 765 in Roman numerals?
DCCLXV.
Is 765 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 765?
765 is a binary palindrome (1011111101).