1804
1804 is a even composite number that follows 1803 and precedes 1805. It is composed of 12 distinct factors: 1, 2, 4, 11, 22, 41, 44, 82, 164, 451, 902, 1804. Its prime factorization can be written as 2^2 × 11 × 41. 1804 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1804 is represented as 11100001100 in binary and 70C in hexadecimal. Historically, it is written as MDCCCIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 11 × 41) reveals 4 prime building blocks.
Divisible by 2
1804 ends in 4, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
1804 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 13 is not a multiple of 9.
Divisible by 10
1804 does not end in 0.
Divisible by 11
The alternating digit sum -11 is a multiple of 11.
Deficient classification and digit analytics place 1804 within several notable number theory sequences:
Timeline
Deep dive
How 1804 breaks down
1804 carries 12 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 1724, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100001100 supports bitwise reasoning, hexadecimal 70C aligns with computing notation, and the Roman numeral MDCCCIV keeps the encyclopedic tradition alive. These attributes make 1804 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1804 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1799–1809) to tune search ranges, and educators feature 1804 in worksheets about factor trees. Its binary footprint of length 11 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 1804 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 1804
Is 1804 a prime number?
1804 is composite with 12 total factors and the prime factorization 2^2 × 11 × 41.
What is the prime factorization of 1804?
It breaks down as 2^2 × 11 × 41, multiplying the primes 2 × 2 × 11 × 41.
How is 1804 represented in binary and hexadecimal?
1804 converts to 11100001100 in binary and 70C in hexadecimal, which are helpful for computer science applications.
Is 1804 a perfect square, cube, or triangular number?
1804 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1804?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.