The number 8640
8640 is a composite number with 56 divisors. Its prime factorisation is × × 5. Divisors (56): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 8640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8640: a Harshad number: divisible by its digit sum 18.
- 2
8640 is composite. Its prime factorisation is
- 3
The divisors add up to 30480; without 8640 itself that is 21840, so 8640 is abundant (21840 is more than 8640). Euler's totient φ(8640) = 2304 numbers up to 8640 share no factor with it.
- 4
The digits of 8640 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 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8640 = 2^{6} \times 3^{3} \times 5 \]8640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 30480 |
| Euler totient φ(n) | 2304 |
| Square | 74649600 |
| Cube | 644972544000 |
| Square root | 92.951600 (= 24√15) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 8.64 × |
8640 in other forms
| Form | Value |
|---|---|
| In words | eight thousand six hundred and forty |
| Binary (base 2) | 10000111000000 |
| Octal (base 8) | 20700 |
| Hexadecimal (base 16) | 21C0 |
| Base 3 | 102212000 |
| As time | 8640 seconds = 2 h 24 min 0 s |
Is 8640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8640 ÷ 2 = 4320) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8640 ÷ 3 = 2880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8640 ÷ 4 = 2160) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8640 ÷ 5 = 1728) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8640 ÷ 6 = 1440) | 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 (8640 ÷ 8 = 1080) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8640 ÷ 9 = 960) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8640 ÷ 10 = 864) | 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 (8640 ÷ 12 = 720) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8640 a prime number?
No. 8640 = × × 5, so it is divisible by 2.
What are the factors of 8640?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 192, 216, 240, 270, 288, 320, 360, 432, 480, 540, 576, 720, 864, 960, 1080, 1440, 1728, 2160, 2880, 4320, 8640.
What is 8640 in binary?
10000111000000 (hexadecimal 21C0, octal 20700).
What is the square root of 8640?
About 92.9516, exactly 24√15.
Is 8640 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8640?
8640 is a Harshad number: divisible by its digit sum 18.