The number 12864
12864 is a composite number with 28 divisors. Its prime factorisation is × 3 × 67. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 67, 96, 134, 192 … 12864.
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How to work it out
- 1
12864 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
12864 is composite. Its prime factorisation is
- 3
The divisors add up to 34544; without 12864 itself that is 21680, so 12864 is abundant (21680 is more than 12864). Euler's totient φ(12864) = 4224 numbers up to 12864 share no factor with it.
- 4
The digits of 12864 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12864 = 2^{6} \times 3 \times 67 \]12864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 34544 |
| Euler totient φ(n) | 4224 |
| Square | 165482496 |
| Cube | 2128766828544 |
| Square root | 113.419575 (= 8√201) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 24 |
| Scientific notation | 1.2864 × |
12864 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand eight hundred and sixty-four |
| Binary (base 2) | 11001001000000 |
| Octal (base 8) | 31100 |
| Hexadecimal (base 16) | 3240 |
| Base 3 | 122122110 |
| As time | 12864 seconds = 3 h 34 min 24 s |
Is 12864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12864 ÷ 2 = 6432) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12864 ÷ 3 = 4288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12864 ÷ 4 = 3216) | 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 (12864 ÷ 6 = 2144) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (12864 ÷ 8 = 1608) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12864 ÷ 12 = 1072) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12864 a prime number?
No. 12864 = × 3 × 67, so it is divisible by 2.
What are the factors of 12864?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 67, 96, 134, 192, 201, 268, 402, 536, 804, 1072, 1608, 2144, 3216, 4288, 6432, 12864.
What is 12864 in binary?
11001001000000 (hexadecimal 3240, octal 31100).
What is the square root of 12864?
About 113.4196, exactly 8√201.
Is 12864 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 12864?
It is a composite number with 28 divisors.