8004
8004 is a even composite number that follows 8003 and precedes 8005. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004. Its prime factorization can be written as 2^2 × 3 × 23 × 29. 8004 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8004 is represented as 1111101000100 in binary and 1F44 in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 23 × 29) reveals 5 prime building blocks.
Divisible by 2
8004 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
8004 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
8004 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 8004 within several notable number theory sequences:
Timeline
Deep dive
How 8004 breaks down
8004 carries 24 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 12156, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111101000100 supports bitwise reasoning, hexadecimal 1F44 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8004 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8004 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7999–8009) to tune search ranges, and educators feature 8004 in worksheets about factor trees. Its binary footprint of length 13 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 8004 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 8004
Is 8004 a prime number?
8004 is composite with 24 total factors and the prime factorization 2^2 × 3 × 23 × 29.
What is the prime factorization of 8004?
It breaks down as 2^2 × 3 × 23 × 29, multiplying the primes 2 × 2 × 3 × 23 × 29.
How is 8004 represented in binary and hexadecimal?
8004 converts to 1111101000100 in binary and 1F44 in hexadecimal, which are helpful for computer science applications.
Is 8004 a perfect square, cube, or triangular number?
8004 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8004?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.