820
820 is a even composite number that follows 819 and precedes 821. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820. Its prime factorization can be written as 2^2 × 5 × 41. 820 is classified as a abundant number based on the sum of its proper divisors. In computer science, 820 is represented as 1100110100 in binary and 334 in hexadecimal. Historically, it is written as DCCCXX in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 41) reveals 4 prime building blocks.
Divisible by 2
820 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 20 form a multiple of 4.
Divisible by 5
820 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
820 ends in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 820 within several notable number theory sequences:
Timeline
Deep dive
How 820 breaks down
820 carries 12 distinct factors and a digit signature of 10 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 944, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100110100 supports bitwise reasoning, hexadecimal 334 aligns with computing notation, and the Roman numeral DCCCXX keeps the encyclopedic tradition alive. These attributes make 820 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 820 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (815–825) to tune search ranges, and educators feature 820 in worksheets about factor trees. Its binary footprint of length 10 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 820 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 820
Is 820 a prime number?
820 is composite with 12 total factors and the prime factorization 2^2 × 5 × 41.
What is the prime factorization of 820?
It breaks down as 2^2 × 5 × 41, multiplying the primes 2 × 2 × 5 × 41.
How is 820 represented in binary and hexadecimal?
820 converts to 1100110100 in binary and 334 in hexadecimal, which are helpful for computer science applications.
Is 820 a perfect square, cube, or triangular number?
820 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 820?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.