2304
2304 is a even composite number that follows 2303 and precedes 2305. It is composed of 27 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304. Its prime factorization can be written as 2^8 × 3^2. 2304 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2304 is represented as 100100000000 in binary and 900 in hexadecimal. Historically, it is written as MMCCCIV in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
27 FactorsProperties
The prime factorization (2^8 × 3^2) reveals 10 prime building blocks.
Divisible by 2
2304 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
2304 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 9 is a multiple of 9.
Divisible by 10
2304 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 2304 within several notable number theory sequences:
Timeline
Deep dive
How 2304 breaks down
2304 carries 27 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4339, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100100000000 supports bitwise reasoning, hexadecimal 900 aligns with computing notation, and the Roman numeral MMCCCIV keeps the encyclopedic tradition alive. These attributes make 2304 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2304 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2299–2309) to tune search ranges, and educators feature 2304 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, Perfect squares) help historians, numerologists, and trivia writers tie 2304 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 2304
Is 2304 a prime number?
2304 is composite with 27 total factors and the prime factorization 2^8 × 3^2.
What is the prime factorization of 2304?
It breaks down as 2^8 × 3^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3.
How is 2304 represented in binary and hexadecimal?
2304 converts to 100100000000 in binary and 900 in hexadecimal, which are helpful for computer science applications.
Is 2304 a perfect square, cube, or triangular number?
2304 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2304?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.