Number dictionary · Exact arithmetic
729: factors and number facts
seven hundred twenty-nine is an odd number and is composite. Its 7 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred twenty-nine
- Roman numeral
- DCCXXIX
- Prime factorization
- 3^6
- Digital root
- 9
All factors of 729
A positive factor divides 729 with no remainder. In ascending order, the complete list is:
1, 3, 9, 27, 81, 243, 729
Factor pairs
- 1 × 729 = 729
- 3 × 243 = 729
- 9 × 81 = 729
- 27 × 27 = 729
Each pair describes an arrangement of 729 items into equal rows. The 27 × 27 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 7
- Sum of all divisors
- 1093
- Sum excluding 729
- 364
- Classification
- deficient
729 is deficient because its proper divisors add to 364, which is less than 729.
Prime factorization of 729
729 = 3^6
Repeated division, step by step
- 729 ÷ 3 = 243
- 243 ÷ 3 = 81
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 729. An exponent records how many times the same prime occurs. The divisor-count calculation is (6 + 1) = 7.
The preceding prime is 727. The next larger prime is 733. The factor list above explains why 729 is composite.
Learn the factorization method729 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred twenty-nine |
| Roman numeral | DCCXXIX |
| Binary (base 2) | 1011011001 |
| Octal (base 8) | 1331 |
| Decimal (base 10) | 729 |
| Hexadecimal (base 16) | 2D9 |
Check the binary conversion
Read 1011011001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 128 + 64 + 16 + 8 + 1 = 729
Check the hexadecimal conversion
2 × 16^2 + 13 × 16^1 + 9 × 16^0 = 729
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 729
- 729 squared
- 729 × 729 = 531,441
- 729 cubed
- 729 × 729 × 729 = 387,420,489
- Square root
- = 27
- Simplified radical
- 27
729 is a perfect square: 27 × 27 = 729. It is also a perfect cube: 9³ = 729.
729 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 729.
Distinguish a square from a square rootMultiplication table for 729
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 | 364 | 1 | No |
| 3 | 243 | 0 | Yes |
| 4 | 182 | 1 | No |
| 5 | 145 | 4 | No |
| 6 | 121 | 3 | No |
| 7 | 104 | 1 | No |
| 8 | 91 | 1 | No |
| 9 | 81 | 0 | Yes |
| 10 | 72 | 9 | No |
| 11 | 66 | 3 | No |
| 12 | 60 | 9 | No |
For example, 729 = 7 × 104 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 729
729 contains 3 decimal digits. Its digit sum is 7 + 2 + 9 = 18.
- 729: 7 + 2 + 9 = 18
- 18: 1 + 8 = 9
The digital root is 9. Reversing its digits gives 927; 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, 729/100 simplifies to 729/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 7.29. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 729 and 12 is 3. Their least common multiple is 2916. The identity GCD × LCM = 729 × 12 = 8748 checks both results.
Work through GCF and LCMQuestions about 729
What are the factors of 729?
The positive factors are 1, 3, 9, 27, 81, 243, 729. There are 7 factors, including 1 and 729.
Is 729 a prime number?
No. 729 is composite: 3^6 = 729.
How do you write 729 in Roman numerals?
729 is DCCXXIX in standard subtractive Roman numeral notation.
What is the binary representation of 729?
729 in decimal is 1011011001 in base 2. Adding its active place values gives 512 + 128 + 64 + 16 + 8 + 1 = 729.
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 729
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 729 add to 18. 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.