The number 6561
6561 is a perfect power () and a perfect square (81²). Its prime factorisation is . Divisors (9): 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6561: a perfect power (); a perfect square (81²).
- 2
6561 is composite. Its prime factorisation is
- 3
The divisors add up to 9841; without 6561 itself that is 3280, so 6561 is deficient (3280 is less than 6561). Euler's totient φ(6561) = 4374 numbers up to 6561 share no factor with it.
- 4
The digits of 6561 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 75 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6561 = 3^{8} \]6561 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 9841 |
| Euler totient φ(n) | 4374 |
| Square | 43046721 |
| Cube | 282429536481 |
| Square root | 81 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 75 |
| Scientific notation | 6.561 × |
| Perfect power |
6561 in other forms
| Form | Value |
|---|---|
| In words | six thousand five hundred and sixty-one |
| Binary (base 2) | 1100110100001 |
| Octal (base 8) | 14641 |
| Hexadecimal (base 16) | 19A1 |
| Base 3 | 100000000 |
| As time | 6561 seconds = 1 h 49 min 21 s |
Is 6561 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6561 ÷ 3 = 2187) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (6561 ÷ 9 = 729) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6561 a prime number?
No. 6561 = , so it is divisible by 3.
What are the factors of 6561?
1, 3, 9, 27, 81, 243, 729, 2187, 6561.
What is 6561 in binary?
1100110100001 (hexadecimal 19A1, octal 14641).
What is the square root of 6561?
81, because 81 × 81 = 6561.
Is 6561 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 6561?
6561 is a perfect power (); a perfect square (81²).