The number 27680
27680 is a composite number with 24 divisors. Its prime factorisation is × 5 × 173. Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 173, 346, 692, 865 … 27680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
27680 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
27680 is composite. Its prime factorisation is
- 3
The divisors add up to 65772; without 27680 itself that is 38092, so 27680 is abundant (38092 is more than 27680). Euler's totient φ(27680) = 11008 numbers up to 27680 share no factor with it.
- 4
The digits of 27680 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 152 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27680 = 2^{5} \times 5 \times 173 \]27680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 65772 |
| Euler totient φ(n) | 11008 |
| Square | 766182400 |
| Cube | 21207928832000 |
| Square root | 166.373075 (= 4√1730) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 152 |
| Scientific notation | 2.768 × |
27680 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand six hundred and eighty |
| Binary (base 2) | 110110000100000 |
| Octal (base 8) | 66040 |
| Hexadecimal (base 16) | 6C20 |
| Base 3 | 1101222012 |
| As time | 27680 seconds = 7 h 41 min 20 s |
Is 27680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27680 ÷ 2 = 13840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27680 ÷ 4 = 6920) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27680 ÷ 5 = 5536) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (27680 ÷ 8 = 3460) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (27680 ÷ 10 = 2768) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27680 a prime number?
No. 27680 = × 5 × 173, so it is divisible by 2.
What are the factors of 27680?
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 173, 346, 692, 865, 1384, 1730, 2768, 3460, 5536, 6920, 13840, 27680.
What is 27680 in binary?
110110000100000 (hexadecimal 6C20, octal 66040).
What is the square root of 27680?
About 166.3731, exactly 4√1730.
Is 27680 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 27680?
It is a composite number with 24 divisors.