2808
2808 is a even composite number that follows 2807 and precedes 2809. It is composed of 32 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 104, 108, 117, 156, 216, 234, 312, 351, 468, 702, 936, 1404, 2808. Its prime factorization can be written as 2^3 × 3^3 × 13. 2808 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2808 is represented as 101011111000 in binary and AF8 in hexadecimal. Historically, it is written as MMDCCCVIII in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3^3 × 13) reveals 7 prime building blocks.
Divisible by 2
2808 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
2808 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 18 is a multiple of 9.
Divisible by 10
2808 does not end in 0.
Divisible by 11
The alternating digit sum -14 is not a multiple of 11.
Abundant classification and digit analytics place 2808 within several notable number theory sequences:
Timeline
Deep dive
How 2808 breaks down
2808 carries 32 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 5592, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101011111000 supports bitwise reasoning, hexadecimal AF8 aligns with computing notation, and the Roman numeral MMDCCCVIII keeps the encyclopedic tradition alive. These attributes make 2808 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2808 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2803–2813) to tune search ranges, and educators feature 2808 in worksheets about factor trees. Its binary footprint of length 12 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 2808 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 2808
Is 2808 a prime number?
2808 is composite with 32 total factors and the prime factorization 2^3 × 3^3 × 13.
What is the prime factorization of 2808?
It breaks down as 2^3 × 3^3 × 13, multiplying the primes 2 × 2 × 2 × 3 × 3 × 3 × 13.
How is 2808 represented in binary and hexadecimal?
2808 converts to 101011111000 in binary and AF8 in hexadecimal, which are helpful for computer science applications.
Is 2808 a perfect square, cube, or triangular number?
2808 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2808?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.