The number 1089
1089 is a perfect square (33²). Its prime factorisation is × . Divisors (9): 1, 3, 9, 11, 33, 99, 121, 363, 1089.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1089: a perfect square (33²).
- 2
1089 is composite. Its prime factorisation is
- 3
The divisors add up to 1729; without 1089 itself that is 640, so 1089 is deficient (640 is less than 1089). Euler's totient φ(1089) = 660 numbers up to 1089 share no factor with it.
- 4
The digits of 1089 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1089 = 3^{2} \times 11^{2} \]1089 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 1729 |
| Euler totient φ(n) | 660 |
| Square | 1185921 |
| Cube | 1291467969 |
| Square root | 33 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.089 × |
| Perfect power |
1089 in other forms
| Form | Value |
|---|---|
| In words | one thousand and eighty-nine |
| Roman numerals | MLXXXIX |
| Binary (base 2) | 10001000001 |
| Octal (base 8) | 2101 |
| Hexadecimal (base 16) | 441 |
| Base 3 | 1111100 |
| As time | 1089 seconds = 18 min 9 s |
Is 1089 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 (1089 ÷ 3 = 363) | 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 4) | 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 (1089 ÷ 9 = 121) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1089 ÷ 11 = 99) | 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 1089 a prime number?
No. 1089 = × , so it is divisible by 3.
What are the factors of 1089?
1, 3, 9, 11, 33, 99, 121, 363, 1089.
What is 1089 in binary?
10001000001 (hexadecimal 441, octal 2101).
What is the square root of 1089?
33, because 33 × 33 = 1089.
What is 1089 in Roman numerals?
MLXXXIX.
Is 1089 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1089?
1089 is a perfect square (33²).