512
512 is a even composite number that follows 511 and precedes 513. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. Its prime factorization can be written as 2^9. 512 is classified as a deficient number based on the sum of its proper divisors. In computer science, 512 is represented as 1000000000 in binary and 200 in hexadecimal. Historically, it is written as DXII in Roman numerals. It also belongs to the perfect cube sequence.
Factor Analysis
10 FactorsProperties
The prime factorization (2^9) reveals 9 prime building blocks.
Divisible by 2
512 ends in 2, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 12 form a multiple of 4.
Divisible by 5
512 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 8 is not a multiple of 9.
Divisible by 10
512 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Deficient classification and digit analytics place 512 within several notable number theory sequences:
Timeline
Deep dive
How 512 breaks down
512 carries 10 distinct factors and a digit signature of 8 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 511, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000000000 supports bitwise reasoning, hexadecimal 200 aligns with computing notation, and the Roman numeral DXII keeps the encyclopedic tradition alive. These attributes make 512 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 512 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (507–517) to tune search ranges, and educators feature 512 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, Perfect cubes) help historians, numerologists, and trivia writers tie 512 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 512
Is 512 a prime number?
512 is composite with 10 total factors and the prime factorization 2^9.
What is the prime factorization of 512?
It breaks down as 2^9, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
How is 512 represented in binary and hexadecimal?
512 converts to 1000000000 in binary and 200 in hexadecimal, which are helpful for computer science applications.
Is 512 a perfect square, cube, or triangular number?
512 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 512?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.