The number 21760
21760 is a composite number with 36 divisors. Its prime factorisation is × 5 × 17. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85 … 21760.
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How to work it out
- 1
What is special about 21760: a Harshad number: divisible by its digit sum 16.
- 2
21760 is composite. Its prime factorisation is
- 3
The divisors add up to 55188; without 21760 itself that is 33428, so 21760 is abundant (33428 is more than 21760). Euler's totient φ(21760) = 8192 numbers up to 21760 share no factor with it.
- 4
The digits of 21760 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 17 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21760 = 2^{8} \times 5 \times 17 \]21760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 55188 |
| Euler totient φ(n) | 8192 |
| Square | 473497600 |
| Cube | 10303307776000 |
| Square root | 147.512711 (= 16√85) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 17 |
| Scientific notation | 2.176 × |
21760 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand seven hundred and sixty |
| Binary (base 2) | 101010100000000 |
| Octal (base 8) | 52400 |
| Hexadecimal (base 16) | 5500 |
| Base 3 | 1002211221 |
| As time | 21760 seconds = 6 h 2 min 40 s |
Is 21760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21760 ÷ 2 = 10880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21760 ÷ 4 = 5440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21760 ÷ 5 = 4352) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (21760 ÷ 8 = 2720) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21760 ÷ 10 = 2176) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21760 a prime number?
No. 21760 = × 5 × 17, so it is divisible by 2.
What are the factors of 21760?
1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 128, 136, 160, 170, 256, 272, 320, 340, 544, 640, 680, 1088, 1280, 1360, 2176, 2720, 4352, 5440, 10880, 21760.
What is 21760 in binary?
101010100000000 (hexadecimal 5500, octal 52400).
What is the square root of 21760?
About 147.5127, exactly 16√85.
Is 21760 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 21760?
21760 is a Harshad number: divisible by its digit sum 16.