The number 32766
32766 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 43 × 127. Divisors (16): 1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766.
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How to work it out
- 1
32766 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32766 is composite. Its prime factorisation is
- 3
The divisors add up to 67584; without 32766 itself that is 34818, so 32766 is abundant (34818 is more than 32766). Euler's totient φ(32766) = 10584 numbers up to 32766 share no factor with it.
- 4
The digits of 32766 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 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32766 = 2 \times 3 \times 43 \times 127 \]
32766 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 67584 |
| Euler totient φ(n) | 10584 |
| Square | 1073610756 |
| Cube | 35177930031096 |
| Square root | 181.013812 |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.2766 × |
32766 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and sixty-six |
| Binary (base 2) | 111111111111110 |
| Octal (base 8) | 77776 |
| Hexadecimal (base 16) | 7FFE |
| Base 3 | 1122221120 |
| As time | 32766 seconds = 9 h 6 min 6 s |
Is 32766 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32766 ÷ 2 = 16383) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32766 ÷ 3 = 10922) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32766 ÷ 6 = 5461) | 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 6) | 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 6) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32766 a prime number?
No. 32766 = 2 × 3 × 43 × 127, so it is divisible by 2.
What are the factors of 32766?
1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383, 32766.
What is 32766 in binary?
111111111111110 (hexadecimal 7FFE, octal 77776).
What is the square root of 32766?
About 181.0138.
Is 32766 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 32766?
It is a composite number with 16 divisors.