55536
55536 is a even composite number that follows 55535 and precedes 55537. It is composed of 40 distinct factors: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 89, 104, 156, 178, 208, 267, 312, 356, 534, 624, 712, 1068, 1157, 1424, 2136, 2314, 3471, 4272, 4628, 6942, 9256, 13884, 18512, 27768, 55536. Its prime factorization can be written as 2^4 × 3 × 13 × 89. 55536 is classified as a abundant number based on the sum of its proper divisors. In computer science, 55536 is represented as 1101100011110000 in binary and D8F0 in hexadecimal.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3 × 13 × 89) reveals 7 prime building blocks.
Divisible by 2
55536 ends in 6, so it is even.
Divisible by 3
The digit sum 24 is a multiple of 3.
Divisible by 4
The last two digits 36 form a multiple of 4.
Divisible by 5
55536 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 24 is not a multiple of 9.
Divisible by 10
55536 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 55536 within several notable number theory sequences:
Timeline
Deep dive
How 55536 breaks down
55536 carries 40 distinct factors and a digit signature of 24 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 100704, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101100011110000 supports bitwise reasoning, hexadecimal D8F0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 55536 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 55536 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (55531–55541) to tune search ranges, and educators feature 55536 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 55536 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 55536
Is 55536 a prime number?
55536 is composite with 40 total factors and the prime factorization 2^4 × 3 × 13 × 89.
What is the prime factorization of 55536?
It breaks down as 2^4 × 3 × 13 × 89, multiplying the primes 2 × 2 × 2 × 2 × 3 × 13 × 89.
How is 55536 represented in binary and hexadecimal?
55536 converts to 1101100011110000 in binary and D8F0 in hexadecimal, which are helpful for computer science applications.
Is 55536 a perfect square, cube, or triangular number?
55536 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 55536?
The digits sum to 24, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.