804
804 is a even composite number that follows 803 and precedes 805. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804. Its prime factorization can be written as 2^2 × 3 × 67. 804 is classified as a abundant number based on the sum of its proper divisors. In computer science, 804 is represented as 1100100100 in binary and 324 in hexadecimal. Historically, it is written as DCCCIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 67) reveals 4 prime building blocks.
Divisible by 2
804 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
804 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 12 is not a multiple of 9.
Divisible by 10
804 does not end in 0.
Divisible by 11
The alternating digit sum 12 is not a multiple of 11.
Abundant classification and digit analytics place 804 within several notable number theory sequences:
Timeline
Deep dive
How 804 breaks down
804 carries 12 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1100, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100100 supports bitwise reasoning, hexadecimal 324 aligns with computing notation, and the Roman numeral DCCCIV keeps the encyclopedic tradition alive. These attributes make 804 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 804 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (799–809) to tune search ranges, and educators feature 804 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, Abundant numbers) help historians, numerologists, and trivia writers tie 804 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 804
Is 804 a prime number?
804 is composite with 12 total factors and the prime factorization 2^2 × 3 × 67.
What is the prime factorization of 804?
It breaks down as 2^2 × 3 × 67, multiplying the primes 2 × 2 × 3 × 67.
How is 804 represented in binary and hexadecimal?
804 converts to 1100100100 in binary and 324 in hexadecimal, which are helpful for computer science applications.
Is 804 a perfect square, cube, or triangular number?
804 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 804?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.