The number 58560
58560 is a composite number with 56 divisors. Its prime factorisation is × 3 × 5 × 61. Divisors (56): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 58560.
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How to work it out
- 1
What is special about 58560: a Harshad number: divisible by its digit sum 24.
- 2
58560 is composite. Its prime factorisation is
- 3
The divisors add up to 188976; without 58560 itself that is 130416, so 58560 is abundant (130416 is more than 58560). Euler's totient φ(58560) = 15360 numbers up to 58560 share no factor with it.
- 4
The digits of 58560 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 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 58560 = 2^{6} \times 3 \times 5 \times 61 \]58560 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 188976 |
| Euler totient φ(n) | 15360 |
| Square | 3429273600 |
| Cube | 200818262016000 |
| Square root | 241.991735 (= 8√915) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 135 |
| Scientific notation | 5.856 × |
58560 in other forms
| Form | Value |
|---|---|
| In words | fifty-eight thousand five hundred and sixty |
| Binary (base 2) | 1110010011000000 |
| Octal (base 8) | 162300 |
| Hexadecimal (base 16) | E4C0 |
| Base 3 | 2222022220 |
| As time | 58560 seconds = 16 h 16 min 0 s |
Is 58560 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (58560 ÷ 2 = 29280) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (58560 ÷ 3 = 19520) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (58560 ÷ 4 = 14640) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (58560 ÷ 5 = 11712) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (58560 ÷ 6 = 9760) | 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 (58560 ÷ 8 = 7320) | 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 | Yes (58560 ÷ 10 = 5856) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (58560 ÷ 12 = 4880) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 58560 a prime number?
No. 58560 = × 3 × 5 × 61, so it is divisible by 2.
What are the factors of 58560?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 61, 64, 80, 96, 120, 122, 160, 183, 192, 240, 244, 305, 320, 366, 480, 488, 610, 732, 915, 960, 976, 1220, 1464, 1830, 1952, 2440, 2928, 3660, 3904, 4880, 5856, 7320, 9760, 11712, 14640, 19520, 29280, 58560.
What is 58560 in binary?
1110010011000000 (hexadecimal E4C0, octal 162300).
What is the square root of 58560?
About 241.9917, exactly 8√915.
Is 58560 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 58560?
58560 is a Harshad number: divisible by its digit sum 24.