2880
2880 is a even composite number that follows 2879 and precedes 2881. It is composed of 42 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 144, 160, 180, 192, 240, 288, 320, 360, 480, 576, 720, 960, 1440, 2880. Its prime factorization can be written as 2^6 × 3^2 × 5. 2880 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2880 is represented as 101101000000 in binary and B40 in hexadecimal. Historically, it is written as MMDCCCLXXX in Roman numerals.
Factor Analysis
42 FactorsProperties
The prime factorization (2^6 × 3^2 × 5) reveals 9 prime building blocks.
Divisible by 2
2880 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 80 form a multiple of 4.
Divisible by 5
2880 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
2880 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 2880 within several notable number theory sequences:
Timeline
Deep dive
How 2880 breaks down
2880 carries 42 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 7026, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101101000000 supports bitwise reasoning, hexadecimal B40 aligns with computing notation, and the Roman numeral MMDCCCLXXX keeps the encyclopedic tradition alive. These attributes make 2880 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2880 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2875–2885) to tune search ranges, and educators feature 2880 in worksheets about factor trees. Its binary footprint of length 12 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 2880 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 2880
Is 2880 a prime number?
2880 is composite with 42 total factors and the prime factorization 2^6 × 3^2 × 5.
What is the prime factorization of 2880?
It breaks down as 2^6 × 3^2 × 5, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5.
How is 2880 represented in binary and hexadecimal?
2880 converts to 101101000000 in binary and B40 in hexadecimal, which are helpful for computer science applications.
Is 2880 a perfect square, cube, or triangular number?
2880 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2880?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.