The number 81
81 is a perfect power () and a perfect square (9²). Its prime factorisation is . Divisors (5): 1, 3, 9, 27, 81.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 81: a perfect power (); a perfect square (9²); a Harshad number: divisible by its digit sum 9.
- 2
81 is composite. Its prime factorisation is
- 3
The divisors add up to 121; without 81 itself that is 40, so 81 is deficient (40 is less than 81). Euler's totient φ(81) = 54 numbers up to 81 share no factor with it.
- 4
The digits of 81 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 81 = 3^{4} \]81 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 5 |
| Sum of divisors | 121 |
| Euler totient φ(n) | 54 |
| Square | 6561 |
| Cube | 531441 |
| Square root | 9 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 22 |
| Scientific notation | 8.1 × |
| Perfect power |
81 in other forms
| Form | Value |
|---|---|
| In words | eighty-one |
| Roman numerals | LXXXI |
| Binary (base 2) | 1010001 |
| Octal (base 8) | 121 |
| Hexadecimal (base 16) | 51 |
| Base 3 | 10000 |
| As time | 81 seconds = 1 min 21 s |
Is 81 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 (81 ÷ 3 = 27) | 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 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (81 ÷ 9 = 9) | 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 4) | 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 81 a prime number?
No. 81 = , so it is divisible by 3.
What are the factors of 81?
1, 3, 9, 27, 81.
What is 81 in binary?
1010001 (hexadecimal 51, octal 121).
What is the square root of 81?
9, because 9 × 9 = 81.
What is 81 in Roman numerals?
LXXXI.
Is 81 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 81?
81 is a perfect power (); a perfect square (9²); a Harshad number: divisible by its digit sum 9.