5184
5184 is a even composite number that follows 5183 and precedes 5185. It is composed of 35 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184. Its prime factorization can be written as 2^6 × 3^4. 5184 is classified as a abundant number based on the sum of its proper divisors. In computer science, 5184 is represented as 1010001000000 in binary and 1440 in hexadecimal. It also belongs to the perfect square sequence.
Factor Analysis
35 FactorsProperties
The prime factorization (2^6 × 3^4) reveals 10 prime building blocks.
Divisible by 2
5184 ends in 4, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
5184 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 18 is a multiple of 9.
Divisible by 10
5184 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 5184 within several notable number theory sequences:
Timeline
Deep dive
How 5184 breaks down
5184 carries 35 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 10183, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010001000000 supports bitwise reasoning, hexadecimal 1440 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 5184 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 5184 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (5179–5189) to tune search ranges, and educators feature 5184 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, Perfect squares) help historians, numerologists, and trivia writers tie 5184 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 5184
Is 5184 a prime number?
5184 is composite with 35 total factors and the prime factorization 2^6 × 3^4.
What is the prime factorization of 5184?
It breaks down as 2^6 × 3^4, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3.
How is 5184 represented in binary and hexadecimal?
5184 converts to 1010001000000 in binary and 1440 in hexadecimal, which are helpful for computer science applications.
Is 5184 a perfect square, cube, or triangular number?
5184 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 5184?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.