3584
3584 is a even composite number that follows 3583 and precedes 3585. It is composed of 20 distinct factors: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584. Its prime factorization can be written as 2^9 × 7. 3584 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3584 is represented as 111000000000 in binary and E00 in hexadecimal. Historically, it is written as MMMDLXXXIV in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^9 × 7) reveals 10 prime building blocks.
Divisible by 2
3584 ends in 4, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
3584 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 20 is not a multiple of 9.
Divisible by 10
3584 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 3584 within several notable number theory sequences:
Timeline
Deep dive
How 3584 breaks down
3584 carries 20 distinct factors and a digit signature of 20 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 4600, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111000000000 supports bitwise reasoning, hexadecimal E00 aligns with computing notation, and the Roman numeral MMMDLXXXIV keeps the encyclopedic tradition alive. These attributes make 3584 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3584 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3579–3589) to tune search ranges, and educators feature 3584 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) help historians, numerologists, and trivia writers tie 3584 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 3584
Is 3584 a prime number?
3584 is composite with 20 total factors and the prime factorization 2^9 × 7.
What is the prime factorization of 3584?
It breaks down as 2^9 × 7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7.
How is 3584 represented in binary and hexadecimal?
3584 converts to 111000000000 in binary and E00 in hexadecimal, which are helpful for computer science applications.
Is 3584 a perfect square, cube, or triangular number?
3584 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3584?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.