The number 289
289 is a perfect square (17²). Its prime factorisation is . Divisors (3): 1, 17, 289.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 289: a perfect square (17²); the square of a prime (17²).
- 2
289 is composite. Its prime factorisation is
- 3
The divisors add up to 307; without 289 itself that is 18, so 289 is deficient (18 is less than 289). Euler's totient φ(289) = 272 numbers up to 289 share no factor with it.
- 4
The digits of 289 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 289 = 17^{2} \]289 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 307 |
| Euler totient φ(n) | 272 |
| Square | 83521 |
| Cube | 24137569 |
| Square root | 17 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 29 |
| Scientific notation | 2.89 × |
| Perfect power |
289 in other forms
| Form | Value |
|---|---|
| In words | two hundred and eighty-nine |
| Roman numerals | CCLXXXIX |
| Binary (base 2) | 100100001 |
| Octal (base 8) | 441 |
| Hexadecimal (base 16) | 121 |
| Base 3 | 101201 |
| As time | 289 seconds = 4 min 49 s |
Is 289 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 | No (remainder 1) | 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 1) | 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 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 289 a prime number?
No. 289 = , so it is divisible by 17.
What are the factors of 289?
1, 17, 289.
What is 289 in binary?
100100001 (hexadecimal 121, octal 441).
What is the square root of 289?
17, because 17 × 17 = 289.
What is 289 in Roman numerals?
CCLXXXIX.
Is 289 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 289?
289 is a perfect square (17²); the square of a prime (17²).