Number dictionary · Exact arithmetic
289: factors and number facts
two hundred eighty-nine is an odd number and is composite. Its 3 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred eighty-nine
- Roman numeral
- CCLXXXIX
- Prime factorization
- 17^2
- Digital root
- 1
All factors of 289
A positive factor divides 289 with no remainder. In ascending order, the complete list is:
1, 17, 289
Factor pairs
- 1 × 289 = 289
- 17 × 17 = 289
Each pair describes an arrangement of 289 items into equal rows. The 17 × 17 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 3
- Sum of all divisors
- 307
- Sum excluding 289
- 18
- Classification
- deficient
289 is deficient because its proper divisors add to 18, which is less than 289.
Prime factorization of 289
289 = 17^2
Repeated division, step by step
- 289 ÷ 17 = 17
- 17 ÷ 17 = 1
Multiply the prime divisors in these steps to reconstruct 289. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) = 3.
The preceding prime is 283. The next larger prime is 293. The factor list above explains why 289 is composite.
Learn the factorization method289 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred eighty-nine |
| Roman numeral | CCLXXXIX |
| Binary (base 2) | 100100001 |
| Octal (base 8) | 441 |
| Decimal (base 10) | 289 |
| Hexadecimal (base 16) | 121 |
Check the binary conversion
Read 100100001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 32 + 1 = 289
Check the hexadecimal conversion
1 × 16^2 + 2 × 16^1 + 1 × 16^0 = 289
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 289
- 289 squared
- 289 × 289 = 83,521
- 289 cubed
- 289 × 289 × 289 = 24,137,569
- Square root
- = 17
- Simplified radical
- 17
289 is a perfect square: 17 × 17 = 289. It is not a perfect cube.
289 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 289.
Distinguish a square from a square rootMultiplication table for 289
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 144 | 1 | No |
| 3 | 96 | 1 | No |
| 4 | 72 | 1 | No |
| 5 | 57 | 4 | No |
| 6 | 48 | 1 | No |
| 7 | 41 | 2 | No |
| 8 | 36 | 1 | No |
| 9 | 32 | 1 | No |
| 10 | 28 | 9 | No |
| 11 | 26 | 3 | No |
| 12 | 24 | 1 | No |
For example, 289 = 7 × 41 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 289
289 contains 3 decimal digits. Its digit sum is 2 + 8 + 9 = 19.
- 289: 2 + 8 + 9 = 19
- 19: 1 + 9 = 10
- 10: 1 + 0 = 1
The digital root is 1. Reversing its digits gives 982; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 289/100 simplifies to 289/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 2.89. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 289 and 12 is 1. Their least common multiple is 3468. The identity GCD × LCM = 289 × 12 = 3468 checks both results.
Work through GCF and LCMQuestions about 289
What are the factors of 289?
The positive factors are 1, 17, 289. There are 3 factors, including 1 and 289.
Is 289 a prime number?
No. 289 is composite: 17^2 = 289.
How do you write 289 in Roman numerals?
289 is CCLXXXIX in standard subtractive Roman numeral notation.
What is the binary representation of 289?
289 in decimal is 100100001 in base 2. Adding its active place values gives 256 + 32 + 1 = 289.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 289
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 289 add to 19. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.