1820
1820 is a even composite number that follows 1819 and precedes 1821. It is composed of 24 distinct factors: 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91, 130, 140, 182, 260, 364, 455, 910, 1820. Its prime factorization can be written as 2^2 × 5 × 7 × 13. 1820 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1820 is represented as 11100011100 in binary and 71C in hexadecimal. Historically, it is written as MDCCCXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 5 × 7 × 13) reveals 5 prime building blocks.
Divisible by 2
1820 ends in 0, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
1820 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 11 is not a multiple of 9.
Divisible by 10
1820 ends in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 1820 within several notable number theory sequences:
Timeline
Deep dive
How 1820 breaks down
1820 carries 24 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 2884, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100011100 supports bitwise reasoning, hexadecimal 71C aligns with computing notation, and the Roman numeral MDCCCXX keeps the encyclopedic tradition alive. These attributes make 1820 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1820 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1815–1825) to tune search ranges, and educators feature 1820 in worksheets about factor trees. Its binary footprint of length 11 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 1820 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 1820
Is 1820 a prime number?
1820 is composite with 24 total factors and the prime factorization 2^2 × 5 × 7 × 13.
What is the prime factorization of 1820?
It breaks down as 2^2 × 5 × 7 × 13, multiplying the primes 2 × 2 × 5 × 7 × 13.
How is 1820 represented in binary and hexadecimal?
1820 converts to 11100011100 in binary and 71C in hexadecimal, which are helpful for computer science applications.
Is 1820 a perfect square, cube, or triangular number?
1820 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1820?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.