The number 864
864 is a composite number with 24 divisors. Its prime factorisation is × . Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 864.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 864: a Harshad number: divisible by its digit sum 18.
- 2
864 is composite. Its prime factorisation is
- 3
The divisors add up to 2520; without 864 itself that is 1656, so 864 is abundant (1656 is more than 864). Euler's totient φ(864) = 288 numbers up to 864 share no factor with it.
- 4
The digits of 864 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 116 steps to reach 1.
LaTeX source of the formulas on this page
\[ 864 = 2^{5} \times 3^{3} \]864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 2520 |
| Euler totient φ(n) | 288 |
| Square | 746496 |
| Cube | 644972544 |
| Square root | 29.393877 (= 12√6) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 116 |
| Scientific notation | 8.64 × |
864 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and sixty-four |
| Roman numerals | DCCCLXIV |
| Binary (base 2) | 1101100000 |
| Octal (base 8) | 1540 |
| Hexadecimal (base 16) | 360 |
| Base 3 | 1012000 |
| As time | 864 seconds = 14 min 24 s |
Is 864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (864 ÷ 2 = 432) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (864 ÷ 3 = 288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (864 ÷ 4 = 216) | 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 (864 ÷ 6 = 144) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (864 ÷ 8 = 108) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (864 ÷ 9 = 96) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (864 ÷ 12 = 72) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 864 a prime number?
No. 864 = × , so it is divisible by 2.
What are the factors of 864?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.
What is 864 in binary?
1101100000 (hexadecimal 360, octal 1540).
What is the square root of 864?
About 29.3939, exactly 12√6.
What is 864 in Roman numerals?
DCCCLXIV.
Is 864 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 864?
864 is a Harshad number: divisible by its digit sum 18.