The number 55680
55680 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 29. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32 … 55680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 55680: a Harshad number: divisible by its digit sum 24.
- 2
55680 is composite. Its prime factorisation is
- 3
The divisors add up to 183600; without 55680 itself that is 127920, so 55680 is abundant (127920 is more than 55680). Euler's totient φ(55680) = 14336 numbers up to 55680 share no factor with it.
- 4
The digits of 55680 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 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 55680 = 2^{7} \times 3 \times 5 \times 29 \]55680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 183600 |
| Euler totient φ(n) | 14336 |
| Square | 3100262400 |
| Cube | 172622610432000 |
| Square root | 235.966099 (= 8√870) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 34 |
| Scientific notation | 5.568 × |
55680 in other forms
| Form | Value |
|---|---|
| In words | fifty-five thousand six hundred and eighty |
| Binary (base 2) | 1101100110000000 |
| Octal (base 8) | 154600 |
| Hexadecimal (base 16) | D980 |
| Base 3 | 2211101020 |
| As time | 55680 seconds = 15 h 28 min 0 s |
Is 55680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (55680 ÷ 2 = 27840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (55680 ÷ 3 = 18560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (55680 ÷ 4 = 13920) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (55680 ÷ 5 = 11136) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (55680 ÷ 6 = 9280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (55680 ÷ 8 = 6960) | 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 (55680 ÷ 10 = 5568) | 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 (55680 ÷ 12 = 4640) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 55680 a prime number?
No. 55680 = × 3 × 5 × 29, so it is divisible by 2.
What are the factors of 55680?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 64, 80, 87, 96, 116, 120, 128, 145, 160, 174, 192, 232, 240, 290, 320, 348, 384, 435, 464, 480, 580, 640, 696, 870, 928, 960, 1160, 1392, 1740, 1856, 1920, 2320, 2784, 3480, 3712, 4640, 5568, 6960, 9280, 11136, 13920, 18560, 27840, 55680.
What is 55680 in binary?
1101100110000000 (hexadecimal D980, octal 154600).
What is the square root of 55680?
About 235.9661, exactly 8√870.
Is 55680 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 55680?
55680 is a Harshad number: divisible by its digit sum 24.