The number 57600
57600 is a perfect square (240²). Its prime factorisation is × × . Divisors (81): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 57600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 57600: a perfect square (240²); a Harshad number: divisible by its digit sum 18.
- 2
57600 is composite. Its prime factorisation is
- 3
The divisors add up to 205933; without 57600 itself that is 148333, so 57600 is abundant (148333 is more than 57600). Euler's totient φ(57600) = 15360 numbers up to 57600 share no factor with it.
- 4
The digits of 57600 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 60 steps to reach 1.
LaTeX source of the formulas on this page
\[ 57600 = 2^{8} \times 3^{2} \times 5^{2} \]57600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 81 |
| Sum of divisors | 205933 |
| Euler totient φ(n) | 15360 |
| Square | 3317760000 |
| Cube | 191102976000000 |
| Square root | 240 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 60 |
| Scientific notation | 5.76 × |
| Perfect power |
57600 in other forms
| Form | Value |
|---|---|
| In words | fifty-seven thousand six hundred |
| Binary (base 2) | 1110000100000000 |
| Octal (base 8) | 160400 |
| Hexadecimal (base 16) | E100 |
| Base 3 | 2221000100 |
| As time | 57600 seconds = 16 h 0 min 0 s |
Is 57600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (57600 ÷ 2 = 28800) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (57600 ÷ 3 = 19200) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (57600 ÷ 4 = 14400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (57600 ÷ 5 = 11520) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (57600 ÷ 6 = 9600) | 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 (57600 ÷ 8 = 7200) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (57600 ÷ 9 = 6400) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (57600 ÷ 10 = 5760) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (57600 ÷ 12 = 4800) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 57600 a prime number?
No. 57600 = × × , so it is divisible by 2.
What are the factors of 57600?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 256, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 768, 800, 900, 960, 1152, 1200, 1280, 1440, 1600, 1800, 1920, 2304, 2400, 2880, 3200, 3600, 3840, 4800, 5760, 6400, 7200, 9600, 11520, 14400, 19200, 28800, 57600.
What is 57600 in binary?
1110000100000000 (hexadecimal E100, octal 160400).
What is the square root of 57600?
240, because 240 × 240 = 57600.
Is 57600 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 57600?
57600 is a perfect square (240²); a Harshad number: divisible by its digit sum 18.