Number reference
729 explained.
729: seven hundred twenty-nine, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- seven hundred twenty-nine
- Classification
- composite
- Factors
- 1, 3, 9, 27, 81, 243, 729
- Prime factorization
- 3 × 3 × 3 × 3 × 3 × 3
- Square root
- 27
- Cube root
- 9
- Binary
- 1011011001
- Octal
- 1331
- Hexadecimal
- 2D9
- Roman numeral
- DCCXXIX
- Digit sum
- 18
- Digital root
- 9
What makes 729 notable
- Perfect square. 729 = 27², so a square of side 27 has an area of 729.
- Perfect cube. 729 = 9³, so a cube of edge 9 has a volume of 729.
729 in everyday use
Seven hundred twenty-nine is three to the sixth power, and it appears in Plato's Republic, where Socrates calculates that the just king lives 729 times more pleasantly than the tyrant, a number he links to the days and nights of a year. Because 3⁶ is also 9³ and 27², the number is at once a square, a cube, and a sixth power. In computing it is the number of distinct strings of six ternary digits, and a 27 by 27 grid holds 729 cells.
Its divisors are exactly the powers of three from 1 to 729, seven in all. It is 1000000 in base three, 1011011001 in binary, and 2D9 in hexadecimal. Its digit sum is 18, which is divisible by 9, as the digit-sum rule requires for a multiple of 9. It is one less than 730 = 2 × 5 × 73 and one more than 728 = 2³ × 7 × 13, and the nearest primes are 727 and 733.
Nearby numbers
How to read this page
The factor list shows every way 729 splits into equal whole-number groups — 7 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 729 for contexts that do not use decimal.
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