55328
55328 is a even composite number that follows 55327 and precedes 55329. It is composed of 48 distinct factors: 1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32, 38, 52, 56, 76, 91, 104, 112, 133, 152, 182, 208, 224, 247, 266, 304, 364, 416, 494, 532, 608, 728, 988, 1064, 1456, 1729, 1976, 2128, 2912, 3458, 3952, 4256, 6916, 7904, 13832, 27664, 55328. Its prime factorization can be written as 2^5 × 7 × 13 × 19. 55328 is classified as a abundant number based on the sum of its proper divisors. In computer science, 55328 is represented as 1101100000100000 in binary and D820 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^5 × 7 × 13 × 19) reveals 8 prime building blocks.
Divisible by 2
55328 ends in 8, so it is even.
Divisible by 3
The digit sum 23 is not a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
55328 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 23 is not a multiple of 9.
Divisible by 10
55328 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 55328 within several notable number theory sequences:
Timeline
Deep dive
How 55328 breaks down
55328 carries 48 distinct factors and a digit signature of 23 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 85792, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101100000100000 supports bitwise reasoning, hexadecimal D820 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 55328 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 55328 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (55323–55333) to tune search ranges, and educators feature 55328 in worksheets about factor trees. Its binary footprint of length 16 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 55328 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 55328
Is 55328 a prime number?
55328 is composite with 48 total factors and the prime factorization 2^5 × 7 × 13 × 19.
What is the prime factorization of 55328?
It breaks down as 2^5 × 7 × 13 × 19, multiplying the primes 2 × 2 × 2 × 2 × 2 × 7 × 13 × 19.
How is 55328 represented in binary and hexadecimal?
55328 converts to 1101100000100000 in binary and D820 in hexadecimal, which are helpful for computer science applications.
Is 55328 a perfect square, cube, or triangular number?
55328 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 55328?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.