The number 36864
36864 is a perfect square (192²). Its prime factorisation is × . Divisors (39): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 36864.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 36864: a perfect square (192²).
- 2
36864 is composite. Its prime factorisation is
- 3
The divisors add up to 106483; without 36864 itself that is 69619, so 36864 is abundant (69619 is more than 36864). Euler's totient φ(36864) = 12288 numbers up to 36864 share no factor with it.
- 4
The digits of 36864 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 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 36864 = 2^{12} \times 3^{2} \]36864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 39 |
| Sum of divisors | 106483 |
| Euler totient φ(n) | 12288 |
| Square | 1358954496 |
| Cube | 50096498540544 |
| Square root | 192 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 31 |
| Scientific notation | 3.6864 × |
| Perfect power |
36864 in other forms
| Form | Value |
|---|---|
| In words | thirty-six thousand eight hundred and sixty-four |
| Binary (base 2) | 1001000000000000 |
| Octal (base 8) | 110000 |
| Hexadecimal (base 16) | 9000 |
| Base 3 | 1212120100 |
| As time | 36864 seconds = 10 h 14 min 24 s |
Is 36864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36864 ÷ 2 = 18432) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (36864 ÷ 3 = 12288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (36864 ÷ 4 = 9216) | 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 | Yes (36864 ÷ 6 = 6144) | 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 | Yes (36864 ÷ 8 = 4608) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (36864 ÷ 9 = 4096) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (36864 ÷ 12 = 3072) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 36864 a prime number?
No. 36864 = × , so it is divisible by 2.
What are the factors of 36864?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2048, 2304, 3072, 4096, 4608, 6144, 9216, 12288, 18432, 36864.
What is 36864 in binary?
1001000000000000 (hexadecimal 9000, octal 110000).
What is the square root of 36864?
192, because 192 × 192 = 36864.
Is 36864 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 36864?
36864 is a perfect square (192²).