13804
13804 is a even composite number that follows 13803 and precedes 13805. It is composed of 24 distinct factors: 1, 2, 4, 7, 14, 17, 28, 29, 34, 58, 68, 116, 119, 203, 238, 406, 476, 493, 812, 986, 1972, 3451, 6902, 13804. Its prime factorization can be written as 2^2 × 7 × 17 × 29. 13804 is classified as a abundant number based on the sum of its proper divisors. In computer science, 13804 is represented as 11010111101100 in binary and 35EC in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 7 × 17 × 29) reveals 5 prime building blocks.
Divisible by 2
13804 ends in 4, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
13804 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 16 is not a multiple of 9.
Divisible by 10
13804 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 13804 within several notable number theory sequences:
Timeline
Deep dive
How 13804 breaks down
13804 carries 24 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 16436, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010111101100 supports bitwise reasoning, hexadecimal 35EC aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 13804 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 13804 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (13799–13809) to tune search ranges, and educators feature 13804 in worksheets about factor trees. Its binary footprint of length 14 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 13804 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 13804
Is 13804 a prime number?
13804 is composite with 24 total factors and the prime factorization 2^2 × 7 × 17 × 29.
What is the prime factorization of 13804?
It breaks down as 2^2 × 7 × 17 × 29, multiplying the primes 2 × 2 × 7 × 17 × 29.
How is 13804 represented in binary and hexadecimal?
13804 converts to 11010111101100 in binary and 35EC in hexadecimal, which are helpful for computer science applications.
Is 13804 a perfect square, cube, or triangular number?
13804 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 13804?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.