2184
2184 is a even composite number that follows 2183 and precedes 2185. It is composed of 32 distinct factors: 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184. Its prime factorization can be written as 2^3 × 3 × 7 × 13. 2184 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2184 is represented as 100010001000 in binary and 888 in hexadecimal. Historically, it is written as MMCLXXXIV in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 7 × 13) reveals 6 prime building blocks.
Divisible by 2
2184 ends in 4, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
2184 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 15 is not a multiple of 9.
Divisible by 10
2184 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 2184 within several notable number theory sequences:
Timeline
Deep dive
How 2184 breaks down
2184 carries 32 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 4536, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100010001000 supports bitwise reasoning, hexadecimal 888 aligns with computing notation, and the Roman numeral MMCLXXXIV keeps the encyclopedic tradition alive. These attributes make 2184 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2184 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2179–2189) to tune search ranges, and educators feature 2184 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 2184 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 2184
Is 2184 a prime number?
2184 is composite with 32 total factors and the prime factorization 2^3 × 3 × 7 × 13.
What is the prime factorization of 2184?
It breaks down as 2^3 × 3 × 7 × 13, multiplying the primes 2 × 2 × 2 × 3 × 7 × 13.
How is 2184 represented in binary and hexadecimal?
2184 converts to 100010001000 in binary and 888 in hexadecimal, which are helpful for computer science applications.
Is 2184 a perfect square, cube, or triangular number?
2184 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2184?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.