The number 58320
58320 is a composite number with 70 divisors. Its prime factorisation is × × 5. Divisors (70): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 58320.
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How to work it out
- 1
What is special about 58320: a Harshad number: divisible by its digit sum 18.
- 2
58320 is composite. Its prime factorisation is
- 3
The divisors add up to 203298; without 58320 itself that is 144978, so 58320 is abundant (144978 is more than 58320). Euler's totient φ(58320) = 15552 numbers up to 58320 share no factor with it.
- 4
The digits of 58320 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
\[ 58320 = 2^{4} \times 3^{6} \times 5 \]58320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 70 |
| Sum of divisors | 203298 |
| Euler totient φ(n) | 15552 |
| Square | 3401222400 |
| Cube | 198359290368000 |
| Square root | 241.495342 (= 108√5) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.832 × |
58320 in other forms
| Form | Value |
|---|---|
| In words | fifty-eight thousand three hundred and twenty |
| Binary (base 2) | 1110001111010000 |
| Octal (base 8) | 161720 |
| Hexadecimal (base 16) | E3D0 |
| Base 3 | 2222000000 |
| As time | 58320 seconds = 16 h 12 min 0 s |
Is 58320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (58320 ÷ 2 = 29160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (58320 ÷ 3 = 19440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (58320 ÷ 4 = 14580) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (58320 ÷ 5 = 11664) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (58320 ÷ 6 = 9720) | 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 (58320 ÷ 8 = 7290) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (58320 ÷ 9 = 6480) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (58320 ÷ 10 = 5832) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (58320 ÷ 12 = 4860) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 58320 a prime number?
No. 58320 = × × 5, so it is divisible by 2.
What are the factors of 58320?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 108, 120, 135, 144, 162, 180, 216, 240, 243, 270, 324, 360, 405, 432, 486, 540, 648, 720, 729, 810, 972, 1080, 1215, 1296, 1458, 1620, 1944, 2160, 2430, 2916, 3240, 3645, 3888, 4860, 5832, 6480, 7290, 9720, 11664, 14580, 19440, 29160, 58320.
What is 58320 in binary?
1110001111010000 (hexadecimal E3D0, octal 161720).
What is the square root of 58320?
About 241.4953, exactly 108√5.
Is 58320 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 58320?
58320 is a Harshad number: divisible by its digit sum 18.