728
728 is a even composite number that follows 727 and precedes 729. It is composed of 16 distinct factors: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. Its prime factorization can be written as 2^3 × 7 × 13. 728 is classified as a abundant number based on the sum of its proper divisors. In computer science, 728 is represented as 1011011000 in binary and 2D8 in hexadecimal. Historically, it is written as DCCXXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 7 × 13) reveals 5 prime building blocks.
Divisible by 2
728 ends in 8, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
728 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 17 is not a multiple of 9.
Divisible by 10
728 does not end in 0.
Divisible by 11
The alternating digit sum 13 is not a multiple of 11.
Abundant classification and digit analytics place 728 within several notable number theory sequences:
Timeline
Deep dive
How 728 breaks down
728 carries 16 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 952, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011011000 supports bitwise reasoning, hexadecimal 2D8 aligns with computing notation, and the Roman numeral DCCXXVIII keeps the encyclopedic tradition alive. These attributes make 728 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 728 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (723–733) to tune search ranges, and educators feature 728 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, Abundant numbers) help historians, numerologists, and trivia writers tie 728 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 728
Is 728 a prime number?
728 is composite with 16 total factors and the prime factorization 2^3 × 7 × 13.
What is the prime factorization of 728?
It breaks down as 2^3 × 7 × 13, multiplying the primes 2 × 2 × 2 × 7 × 13.
How is 728 represented in binary and hexadecimal?
728 converts to 1011011000 in binary and 2D8 in hexadecimal, which are helpful for computer science applications.
Is 728 a perfect square, cube, or triangular number?
728 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 728?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.