The number 32768
32768 is a power of 2 (). Its prime factorisation is . Divisors (16): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32768: a power of 2 ().
- 2
32768 is composite. Its prime factorisation is
- 3
The divisors add up to 65535; without 32768 itself that is 32767, so 32768 is deficient (32767 is less than 32768). Euler's totient φ(32768) = 16384 numbers up to 32768 share no factor with it.
- 4
The digits of 32768 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 15 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32768 = 2^{15} \]32768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 65535 |
| Euler totient φ(n) | 16384 |
| Square | 1073741824 |
| Cube | 35184372088832 |
| Square root | 181.019336 (= 128√2) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 15 |
| Scientific notation | 3.2768 × |
| Perfect power |
32768 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand seven hundred and sixty-eight |
| Binary (base 2) | 1000000000000000 |
| Octal (base 8) | 100000 |
| Hexadecimal (base 16) | 8000 |
| Base 3 | 1122221122 |
| As time | 32768 seconds = 9 h 6 min 8 s |
Is 32768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32768 ÷ 2 = 16384) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32768 ÷ 4 = 8192) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (32768 ÷ 8 = 4096) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32768 a prime number?
No. 32768 = , so it is divisible by 2.
What are the factors of 32768?
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
What is 32768 in binary?
1000000000000000 (hexadecimal 8000, octal 100000).
What is the square root of 32768?
About 181.0193, exactly 128√2.
Is 32768 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 32768?
32768 is a power of 2 ().