5280
5280 is a even composite number that follows 5279 and precedes 5281. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640, 5280. Its prime factorization can be written as 2^5 × 3 × 5 × 11. 5280 is classified as a abundant number based on the sum of its proper divisors. In computer science, 5280 is represented as 1010010100000 in binary and 14A0 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^5 × 3 × 5 × 11) reveals 8 prime building blocks.
Divisible by 2
5280 ends in 0, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
5280 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 15 is not a multiple of 9.
Divisible by 10
5280 ends in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Abundant classification and digit analytics place 5280 within several notable number theory sequences:
Timeline
Deep dive
How 5280 breaks down
5280 carries 48 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 12864, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010010100000 supports bitwise reasoning, hexadecimal 14A0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 5280 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 5280 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (5275–5285) to tune search ranges, and educators feature 5280 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) help historians, numerologists, and trivia writers tie 5280 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 5280
Is 5280 a prime number?
5280 is composite with 48 total factors and the prime factorization 2^5 × 3 × 5 × 11.
What is the prime factorization of 5280?
It breaks down as 2^5 × 3 × 5 × 11, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 5 × 11.
How is 5280 represented in binary and hexadecimal?
5280 converts to 1010010100000 in binary and 14A0 in hexadecimal, which are helpful for computer science applications.
Is 5280 a perfect square, cube, or triangular number?
5280 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 5280?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.