The number 9765
9765 is a composite number with 24 divisors. Its prime factorisation is × 5 × 7 × 31. Divisors (24): 1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279 … 9765.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9765 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9765 is composite. Its prime factorisation is
- 3
The divisors add up to 19968; without 9765 itself that is 10203, so 9765 is abundant (10203 is more than 9765). Euler's totient φ(9765) = 4320 numbers up to 9765 share no factor with it.
- 4
The digits of 9765 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 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9765 = 3^{2} \times 5 \times 7 \times 31 \]9765 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 19968 |
| Euler totient φ(n) | 4320 |
| Square | 95355225 |
| Cube | 931143772125 |
| Square root | 98.818015 (= 3√1085) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.765 × |
9765 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and sixty-five |
| Binary (base 2) | 10011000100101 |
| Octal (base 8) | 23045 |
| Hexadecimal (base 16) | 2625 |
| Base 3 | 111101200 |
| As time | 9765 seconds = 2 h 42 min 45 s |
Is 9765 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 (9765 ÷ 3 = 3255) | 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 (9765 ÷ 5 = 1953) | 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 | Yes (9765 ÷ 7 = 1395) | 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 (9765 ÷ 9 = 1085) | 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 8) | 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 9765 a prime number?
No. 9765 = × 5 × 7 × 31, so it is divisible by 3.
What are the factors of 9765?
1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765.
What is 9765 in binary?
10011000100101 (hexadecimal 2625, octal 23045).
What is the square root of 9765?
About 98.8180, exactly 3√1085.
Is 9765 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9765?
It is a composite number with 24 divisors.