507
507 is a odd composite number that follows 506 and precedes 508. It is composed of 6 distinct factors: 1, 3, 13, 39, 169, 507. Its prime factorization can be written as 3 × 13^2. 507 is classified as a deficient number based on the sum of its proper divisors. In computer science, 507 is represented as 111111011 in binary and 1FB in hexadecimal. Historically, it is written as DVII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3 × 13^2) reveals 3 prime building blocks.
Divisible by 2
507 ends in 7, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
507 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 12 is not a multiple of 9.
Divisible by 10
507 does not end in 0.
Divisible by 11
The alternating digit sum 12 is not a multiple of 11.
Deficient classification and digit analytics place 507 within several notable number theory sequences:
Timeline
Deep dive
How 507 breaks down
507 carries 6 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 225, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111011 supports bitwise reasoning, hexadecimal 1FB aligns with computing notation, and the Roman numeral DVII keeps the encyclopedic tradition alive. These attributes make 507 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 507 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (502–512) to tune search ranges, and educators feature 507 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, Deficient numbers) help historians, numerologists, and trivia writers tie 507 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 507
Is 507 a prime number?
507 is composite with 6 total factors and the prime factorization 3 × 13^2.
What is the prime factorization of 507?
It breaks down as 3 × 13^2, multiplying the primes 3 × 13 × 13.
How is 507 represented in binary and hexadecimal?
507 converts to 111111011 in binary and 1FB in hexadecimal, which are helpful for computer science applications.
Is 507 a perfect square, cube, or triangular number?
507 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 507?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.