2820
2820 is a even composite number that follows 2819 and precedes 2821. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 47, 60, 94, 141, 188, 235, 282, 470, 564, 705, 940, 1410, 2820. Its prime factorization can be written as 2^2 × 3 × 5 × 47. 2820 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2820 is represented as 101100000100 in binary and B04 in hexadecimal. Historically, it is written as MMDCCCXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 47) reveals 5 prime building blocks.
Divisible by 2
2820 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
2820 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 12 is not a multiple of 9.
Divisible by 10
2820 ends in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 2820 within several notable number theory sequences:
Timeline
Deep dive
How 2820 breaks down
2820 carries 24 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 5244, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101100000100 supports bitwise reasoning, hexadecimal B04 aligns with computing notation, and the Roman numeral MMDCCCXX keeps the encyclopedic tradition alive. These attributes make 2820 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2820 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2815–2825) to tune search ranges, and educators feature 2820 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 2820 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 2820
Is 2820 a prime number?
2820 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5 × 47.
What is the prime factorization of 2820?
It breaks down as 2^2 × 3 × 5 × 47, multiplying the primes 2 × 2 × 3 × 5 × 47.
How is 2820 represented in binary and hexadecimal?
2820 converts to 101100000100 in binary and B04 in hexadecimal, which are helpful for computer science applications.
Is 2820 a perfect square, cube, or triangular number?
2820 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2820?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.