The number 5880
5880 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × . Divisors (48): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28 … 5880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5880: a Harshad number: divisible by its digit sum 21.
- 2
5880 is composite. Its prime factorisation is
- 3
The divisors add up to 20520; without 5880 itself that is 14640, so 5880 is abundant (14640 is more than 5880). Euler's totient φ(5880) = 1344 numbers up to 5880 share no factor with it.
- 4
The digits of 5880 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 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5880 = 2^{3} \times 3 \times 5 \times 7^{2} \]5880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 20520 |
| Euler totient φ(n) | 1344 |
| Square | 34574400 |
| Cube | 203297472000 |
| Square root | 76.681158 (= 14√30) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 49 |
| Scientific notation | 5.88 × |
5880 in other forms
| Form | Value |
|---|---|
| In words | five thousand eight hundred and eighty |
| Binary (base 2) | 1011011111000 |
| Octal (base 8) | 13370 |
| Hexadecimal (base 16) | 16F8 |
| Base 3 | 22001210 |
| As time | 5880 seconds = 1 h 38 min 0 s |
Is 5880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5880 ÷ 2 = 2940) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5880 ÷ 3 = 1960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5880 ÷ 4 = 1470) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5880 ÷ 5 = 1176) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (5880 ÷ 6 = 980) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (5880 ÷ 7 = 840) | 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 (5880 ÷ 8 = 735) | 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 (5880 ÷ 10 = 588) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5880 ÷ 12 = 490) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5880 a prime number?
No. 5880 = × 3 × 5 × , so it is divisible by 2.
What are the factors of 5880?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 49, 56, 60, 70, 84, 98, 105, 120, 140, 147, 168, 196, 210, 245, 280, 294, 392, 420, 490, 588, 735, 840, 980, 1176, 1470, 1960, 2940, 5880.
What is 5880 in binary?
1011011111000 (hexadecimal 16F8, octal 13370).
What is the square root of 5880?
About 76.6812, exactly 14√30.
Is 5880 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 5880?
5880 is a Harshad number: divisible by its digit sum 21.