The number 32767
32767 is a binary palindrome (111111111111111). Its prime factorisation is 7 × 31 × 151. Divisors (8): 1, 7, 31, 151, 217, 1057, 4681, 32767.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32767: a binary palindrome (111111111111111).
- 2
32767 is composite. Its prime factorisation is
- 3
The divisors add up to 38912; without 32767 itself that is 6145, so 32767 is deficient (6145 is less than 32767). Euler's totient φ(32767) = 27000 numbers up to 32767 share no factor with it.
- 4
The digits of 32767 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32767 = 7 \times 31 \times 151 \]
32767 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 38912 |
| Euler totient φ(n) | 27000 |
| Square | 1073676289 |
| Cube | 35181150961663 |
| Square root | 181.016574 |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.2767 × |
32767 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and sixty-seven |
| Binary (base 2) | 111111111111111 |
| Octal (base 8) | 77777 |
| Hexadecimal (base 16) | 7FFF |
| Base 3 | 1122221121 |
| As time | 32767 seconds = 9 h 6 min 7 s |
Is 32767 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 | Yes (32767 ÷ 7 = 4681) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32767 a prime number?
No. 32767 = 7 × 31 × 151, so it is divisible by 7.
What are the factors of 32767?
1, 7, 31, 151, 217, 1057, 4681, 32767.
What is 32767 in binary?
111111111111111 (hexadecimal 7FFF, octal 77777).
What is the square root of 32767?
About 181.0166.
Is 32767 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 32767?
32767 is a binary palindrome (111111111111111).