55440
55440 is a even composite number that follows 55439 and precedes 55441. It is composed of 120 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 99, 105, 110, 112, 120, 126, 132, 140, 144, 154, 165, 168, 176, 180, 198, 210, 220, 231, 240, 252, 264, 280, 308, 315, 330, 336, 360, 385, 396, 420, 440, 462, 495, 504, 528, 560, 616, 630, 660, 693, 720, 770, 792, 840, 880, 924, 990, 1008, 1155, 1232, 1260, 1320, 1386, 1540, 1584, 1680, 1848, 1980, 2310, 2520, 2640, 2772, 3080, 3465, 3696, 3960, 4620, 5040, 5544, 6160, 6930, 7920, 9240, 11088, 13860, 18480, 27720, 55440. Its prime factorization can be written as 2^4 × 3^2 × 5 × 7 × 11. 55440 is classified as a abundant number based on the sum of its proper divisors. In computer science, 55440 is represented as 1101100010010000 in binary and D890 in hexadecimal.
Factor Analysis
120 FactorsProperties
The prime factorization (2^4 × 3^2 × 5 × 7 × 11) reveals 9 prime building blocks.
Divisible by 2
55440 ends in 0, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
55440 ends in 0, so it is divisible by 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
55440 ends in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 55440 within several notable number theory sequences:
Timeline
Deep dive
How 55440 breaks down
55440 carries 120 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 176688, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101100010010000 supports bitwise reasoning, hexadecimal D890 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 55440 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 55440 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (55435–55445) to tune search ranges, and educators feature 55440 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 55440 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 55440
Is 55440 a prime number?
55440 is composite with 120 total factors and the prime factorization 2^4 × 3^2 × 5 × 7 × 11.
What is the prime factorization of 55440?
It breaks down as 2^4 × 3^2 × 5 × 7 × 11, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 11.
How is 55440 represented in binary and hexadecimal?
55440 converts to 1101100010010000 in binary and D890 in hexadecimal, which are helpful for computer science applications.
Is 55440 a perfect square, cube, or triangular number?
55440 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 55440?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.