509
509 is a odd prime number that follows 508 and precedes 510. As a prime number, 509 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 509. 509 is classified as a deficient number based on the sum of its proper divisors. In computer science, 509 is represented as 111111101 in binary and 1FD in hexadecimal. Historically, it is written as DIX in Roman numerals.
Factor Analysis
2 FactorsProperties
509 is prime, so its only factors are 1 and 509.
Divisible by 2
509 ends in 9, so it is odd.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 09 are not divisible by 4.
Divisible by 5
509 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 14 is not a multiple of 9.
Divisible by 10
509 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 509 within several notable number theory sequences:
Timeline
Deep dive
How 509 breaks down
509 carries 2 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111101 supports bitwise reasoning, hexadecimal 1FD aligns with computing notation, and the Roman numeral DIX keeps the encyclopedic tradition alive. These attributes make 509 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 509 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (504–514) to tune search ranges, and educators feature 509 in worksheets about prime identification. Its binary footprint of length 9 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 509 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 509
Is 509 a prime number?
509 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 509?
509 is already prime, so the factorization is simply 509.
How is 509 represented in binary and hexadecimal?
509 converts to 111111101 in binary and 1FD in hexadecimal, which are helpful for computer science applications.
Is 509 a perfect square, cube, or triangular number?
509 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 509?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.