N
NumberPedia
Menu

© 2025 NumberPedia

Prime Number

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.

Roman Numeral
DIX
LatinClassic
Binary
111111101
Base 2
Hexadecimal
1FD
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count3
Digit Sum14
Digital Root5
Sum of Factors510
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

509 is prime, so its only factors are 1 and 509.

Canonical form
509
509
Divisibility Insights
  • 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.

Sequence Membership

Deficient classification and digit analytics place 509 within several notable number theory sequences:

Prime numbersDeficient numbers
Advertisement

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 (504514) 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.