585
585 is a odd composite number that follows 584 and precedes 586. It is composed of 12 distinct factors: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585. Its prime factorization can be written as 3^2 × 5 × 13. 585 is classified as a deficient number based on the sum of its proper divisors. In computer science, 585 is represented as 1001001001 in binary and 249 in hexadecimal. Historically, it is written as DLXXXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^2 × 5 × 13) reveals 4 prime building blocks.
Divisible by 2
585 ends in 5, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 85 are not divisible by 4.
Divisible by 5
585 ends in 5, so it is divisible by 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
585 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 585 within several notable number theory sequences:
Timeline
Deep dive
How 585 breaks down
585 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 507, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001001001 supports bitwise reasoning, hexadecimal 249 aligns with computing notation, and the Roman numeral DLXXXV keeps the encyclopedic tradition alive. These attributes make 585 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 585 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (580–590) to tune search ranges, and educators feature 585 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) help historians, numerologists, and trivia writers tie 585 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 585
Is 585 a prime number?
585 is composite with 12 total factors and the prime factorization 3^2 × 5 × 13.
What is the prime factorization of 585?
It breaks down as 3^2 × 5 × 13, multiplying the primes 3 × 3 × 5 × 13.
How is 585 represented in binary and hexadecimal?
585 converts to 1001001001 in binary and 249 in hexadecimal, which are helpful for computer science applications.
Is 585 a perfect square, cube, or triangular number?
585 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 585?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.