2800
2800 is a even composite number that follows 2799 and precedes 2801. It is composed of 30 distinct factors: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800. Its prime factorization can be written as 2^4 × 5^2 × 7. 2800 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2800 is represented as 101011110000 in binary and AF0 in hexadecimal. Historically, it is written as MMDCCC in Roman numerals.
Factor Analysis
30 FactorsProperties
The prime factorization (2^4 × 5^2 × 7) reveals 7 prime building blocks.
Divisible by 2
2800 ends in 0, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
2800 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 10 is not a multiple of 9.
Divisible by 10
2800 ends in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Abundant classification and digit analytics place 2800 within several notable number theory sequences:
Timeline
Deep dive
How 2800 breaks down
2800 carries 30 distinct factors and a digit signature of 10 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 4888, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101011110000 supports bitwise reasoning, hexadecimal AF0 aligns with computing notation, and the Roman numeral MMDCCC keeps the encyclopedic tradition alive. These attributes make 2800 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2800 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2795–2805) to tune search ranges, and educators feature 2800 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 2800 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 2800
Is 2800 a prime number?
2800 is composite with 30 total factors and the prime factorization 2^4 × 5^2 × 7.
What is the prime factorization of 2800?
It breaks down as 2^4 × 5^2 × 7, multiplying the primes 2 × 2 × 2 × 2 × 5 × 5 × 7.
How is 2800 represented in binary and hexadecimal?
2800 converts to 101011110000 in binary and AF0 in hexadecimal, which are helpful for computer science applications.
Is 2800 a perfect square, cube, or triangular number?
2800 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2800?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.