504
504 is a even composite number that follows 503 and precedes 505. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. Its prime factorization can be written as 2^3 × 3^2 × 7. 504 is classified as a abundant number based on the sum of its proper divisors. In computer science, 504 is represented as 111111000 in binary and 1F8 in hexadecimal. Historically, it is written as DIV in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 3^2 × 7) reveals 6 prime building blocks.
Divisible by 2
504 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
504 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 9 is a multiple of 9.
Divisible by 10
504 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 504 within several notable number theory sequences:
Timeline
Deep dive
How 504 breaks down
504 carries 24 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1056, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111000 supports bitwise reasoning, hexadecimal 1F8 aligns with computing notation, and the Roman numeral DIV keeps the encyclopedic tradition alive. These attributes make 504 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 504 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (499–509) to tune search ranges, and educators feature 504 in worksheets about factor trees. 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 (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 504 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 504
Is 504 a prime number?
504 is composite with 24 total factors and the prime factorization 2^3 × 3^2 × 7.
What is the prime factorization of 504?
It breaks down as 2^3 × 3^2 × 7, multiplying the primes 2 × 2 × 2 × 3 × 3 × 7.
How is 504 represented in binary and hexadecimal?
504 converts to 111111000 in binary and 1F8 in hexadecimal, which are helpful for computer science applications.
Is 504 a perfect square, cube, or triangular number?
504 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 504?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.