The number 6864
6864 is a composite number with 40 divisors. Its prime factorisation is × 3 × 11 × 13. Divisors (40): 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44 … 6864.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6864: a Harshad number: divisible by its digit sum 24.
- 2
6864 is composite. Its prime factorisation is
- 3
The divisors add up to 20832; without 6864 itself that is 13968, so 6864 is abundant (13968 is more than 6864). Euler's totient φ(6864) = 1920 numbers up to 6864 share no factor with it.
- 4
The digits of 6864 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 106 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6864 = 2^{4} \times 3 \times 11 \times 13 \]6864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 20832 |
| Euler totient φ(n) | 1920 |
| Square | 47114496 |
| Cube | 323393900544 |
| Square root | 82.849261 (= 4√429) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 106 |
| Scientific notation | 6.864 × |
6864 in other forms
| Form | Value |
|---|---|
| In words | six thousand eight hundred and sixty-four |
| Binary (base 2) | 1101011010000 |
| Octal (base 8) | 15320 |
| Hexadecimal (base 16) | 1AD0 |
| Base 3 | 100102020 |
| As time | 6864 seconds = 1 h 54 min 24 s |
Is 6864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (6864 ÷ 2 = 3432) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6864 ÷ 3 = 2288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (6864 ÷ 4 = 1716) | 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 (6864 ÷ 6 = 1144) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (6864 ÷ 8 = 858) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (6864 ÷ 11 = 624) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (6864 ÷ 12 = 572) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6864 a prime number?
No. 6864 = × 3 × 11 × 13, so it is divisible by 2.
What are the factors of 6864?
1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 132, 143, 156, 176, 208, 264, 286, 312, 429, 528, 572, 624, 858, 1144, 1716, 2288, 3432, 6864.
What is 6864 in binary?
1101011010000 (hexadecimal 1AD0, octal 15320).
What is the square root of 6864?
About 82.8493, exactly 4√429.
Is 6864 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 6864?
6864 is a Harshad number: divisible by its digit sum 24.