Number dictionary · Exact arithmetic
789: factors and number facts
seven hundred eighty-nine is an odd number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred eighty-nine
- Roman numeral
- DCCLXXXIX
- Prime factorization
- 3 × 263
- Digital root
- 6
All factors of 789
A positive factor divides 789 with no remainder. In ascending order, the complete list is:
1, 3, 263, 789
Factor pairs
- 1 × 789 = 789
- 3 × 263 = 789
Each pair describes an arrangement of 789 items into equal rows. The pairs have different row and column counts; 789 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 1056
- Sum excluding 789
- 267
- Classification
- deficient
789 is deficient because its proper divisors add to 267, which is less than 789.
Prime factorization of 789
789 = 3 × 263
Repeated division, step by step
- 789 ÷ 3 = 263
- 263 ÷ 263 = 1
Multiply the prime divisors in these steps to reconstruct 789. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 787. The next larger prime is 797. The factor list above explains why 789 is composite.
Learn the factorization method789 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred eighty-nine |
| Roman numeral | DCCLXXXIX |
| Binary (base 2) | 1100010101 |
| Octal (base 8) | 1425 |
| Decimal (base 10) | 789 |
| Hexadecimal (base 16) | 315 |
Check the binary conversion
Read 1100010101 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 256 + 16 + 4 + 1 = 789
Check the hexadecimal conversion
3 × 16^2 + 1 × 16^1 + 5 × 16^0 = 789
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 789
- 789 squared
- 789 × 789 = 622,521
- 789 cubed
- 789 × 789 × 789 = 491,169,069
- Square root
- ≈ 28.089144
- Simplified radical
- √789
789 lies between 784 (28²) and 841 (29²), so it is not a perfect square. It is not a perfect cube.
789 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 789.
Distinguish a square from a square rootMultiplication table for 789
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 | 394 | 1 | No |
| 3 | 263 | 0 | Yes |
| 4 | 197 | 1 | No |
| 5 | 157 | 4 | No |
| 6 | 131 | 3 | No |
| 7 | 112 | 5 | No |
| 8 | 98 | 5 | No |
| 9 | 87 | 6 | No |
| 10 | 78 | 9 | No |
| 11 | 71 | 8 | No |
| 12 | 65 | 9 | No |
For example, 789 = 7 × 112 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 789
789 contains 3 decimal digits. Its digit sum is 7 + 8 + 9 = 24.
- 789: 7 + 8 + 9 = 24
- 24: 2 + 4 = 6
The digital root is 6. Reversing its digits gives 987; 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, 789/100 simplifies to 789/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 7.89. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 789 and 12 is 3. Their least common multiple is 3156. The identity GCD × LCM = 789 × 12 = 9468 checks both results.
Work through GCF and LCMQuestions about 789
What are the factors of 789?
The positive factors are 1, 3, 263, 789. There are 4 factors, including 1 and 789.
Is 789 a prime number?
No. 789 is composite: 3 × 263 = 789.
How do you write 789 in Roman numerals?
789 is DCCLXXXIX in standard subtractive Roman numeral notation.
What is the binary representation of 789?
789 in decimal is 1100010101 in base 2. Adding its active place values gives 512 + 256 + 16 + 4 + 1 = 789.
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 789
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 789 add to 24. 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.