The number 58800
58800 is a composite number with 90 divisors. Its prime factorisation is × 3 × × . Divisors (90): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 58800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 58800: a Harshad number: divisible by its digit sum 21.
- 2
58800 is composite. Its prime factorisation is
- 3
The divisors add up to 219108; without 58800 itself that is 160308, so 58800 is abundant (160308 is more than 58800). Euler's totient φ(58800) = 13440 numbers up to 58800 share no factor with it.
- 4
The digits of 58800 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 58800 = 2^{4} \times 3 \times 5^{2} \times 7^{2} \]58800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 90 |
| Sum of divisors | 219108 |
| Euler totient φ(n) | 13440 |
| Square | 3457440000 |
| Cube | 203297472000000 |
| Square root | 242.487113 (= 140√3) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 104 |
| Scientific notation | 5.88 × |
58800 in other forms
| Form | Value |
|---|---|
| In words | fifty-eight thousand eight hundred |
| Binary (base 2) | 1110010110110000 |
| Octal (base 8) | 162660 |
| Hexadecimal (base 16) | E5B0 |
| Base 3 | 2222122210 |
| As time | 58800 seconds = 16 h 20 min 0 s |
Is 58800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (58800 ÷ 2 = 29400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (58800 ÷ 3 = 19600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (58800 ÷ 4 = 14700) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (58800 ÷ 5 = 11760) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (58800 ÷ 6 = 9800) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (58800 ÷ 7 = 8400) | 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 (58800 ÷ 8 = 7350) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (58800 ÷ 10 = 5880) | 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 (58800 ÷ 12 = 4900) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 58800 a prime number?
No. 58800 = × 3 × × , so it is divisible by 2.
What are the factors of 58800?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 49, 50, 56, 60, 70, 75, 80, 84, 98, 100, 105, 112, 120, 140, 147, 150, 168, 175, 196, 200, 210, 240, 245, 280, 294, 300, 336, 350, 392, 400, 420, 490, 525, 560, 588, 600, 700, 735, 784, 840, 980, 1050, 1176, 1200, 1225, 1400, 1470, 1680, 1960, 2100, 2352, 2450, 2800, 2940, 3675, 3920, 4200, 4900, 5880, 7350, 8400, 9800, 11760, 14700, 19600, 29400, 58800.
What is 58800 in binary?
1110010110110000 (hexadecimal E5B0, octal 162660).
What is the square root of 58800?
About 242.4871, exactly 140√3.
Is 58800 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 58800?
58800 is a Harshad number: divisible by its digit sum 21.