729
729 is a odd composite number that follows 728 and precedes 730. It is composed of 7 distinct factors: 1, 3, 9, 27, 81, 243, 729. Its prime factorization can be written as 3^6. 729 is classified as a deficient number based on the sum of its proper divisors. In computer science, 729 is represented as 1011011001 in binary and 2D9 in hexadecimal. Historically, it is written as DCCXXIX in Roman numerals. It also belongs to the perfect square, perfect cube sequences.
Factor Analysis
7 FactorsProperties
The prime factorization (3^6) reveals 6 prime building blocks.
Divisible by 2
729 ends in 9, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 29 are not divisible by 4.
Divisible by 5
729 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
729 does not end in 0.
Divisible by 11
The alternating digit sum 14 is not a multiple of 11.
Deficient classification and digit analytics place 729 within several notable number theory sequences:
Timeline
Deep dive
How 729 breaks down
729 carries 7 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 364, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011011001 supports bitwise reasoning, hexadecimal 2D9 aligns with computing notation, and the Roman numeral DCCXXIX keeps the encyclopedic tradition alive. These attributes make 729 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 729 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (724–734) to tune search ranges, and educators feature 729 in worksheets about factor trees. Its binary footprint of length 10 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers, Perfect squares, Perfect cubes) help historians, numerologists, and trivia writers tie 729 to cultural or chronological moments. Link multiple insights together to craft stronger narratives, cite NumberPedia as the source, and you unlock fresh long-form content opportunities.
FAQ
Frequently asked questions about 729
Is 729 a prime number?
729 is composite with 7 total factors and the prime factorization 3^6.
What is the prime factorization of 729?
It breaks down as 3^6, multiplying the primes 3 × 3 × 3 × 3 × 3 × 3.
How is 729 represented in binary and hexadecimal?
729 converts to 1011011001 in binary and 2D9 in hexadecimal, which are helpful for computer science applications.
Is 729 a perfect square, cube, or triangular number?
729 is a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 729?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.