The number 32769
32769 is a binary palindrome (1000000000000001). Its prime factorisation is × 11 × 331. Divisors (12): 1, 3, 9, 11, 33, 99, 331, 993, 2979, 3641, 10923, 32769.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32769: a binary palindrome (1000000000000001).
- 2
32769 is composite. Its prime factorisation is
- 3
The divisors add up to 51792; without 32769 itself that is 19023, so 32769 is deficient (19023 is less than 32769). Euler's totient φ(32769) = 19800 numbers up to 32769 share no factor with it.
- 4
The digits of 32769 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 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32769 = 3^{2} \times 11 \times 331 \]32769 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 51792 |
| Euler totient φ(n) | 19800 |
| Square | 1073807361 |
| Cube | 35187593412609 |
| Square root | 181.022098 (= 3√3641) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.2769 × |
32769 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and sixty-nine |
| Binary (base 2) | 1000000000000001 |
| Octal (base 8) | 100001 |
| Hexadecimal (base 16) | 8001 |
| Base 3 | 1122221200 |
| As time | 32769 seconds = 9 h 6 min 9 s |
Is 32769 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 (32769 ÷ 3 = 10923) | 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 | No (remainder 4) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32769 ÷ 9 = 3641) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (32769 ÷ 11 = 2979) | 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 32769 a prime number?
No. 32769 = × 11 × 331, so it is divisible by 3.
What are the factors of 32769?
1, 3, 9, 11, 33, 99, 331, 993, 2979, 3641, 10923, 32769.
What is 32769 in binary?
1000000000000001 (hexadecimal 8001, octal 100001).
What is the square root of 32769?
About 181.0221, exactly 3√3641.
Is 32769 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 32769?
32769 is a binary palindrome (1000000000000001).