821
821 is a odd prime number that follows 820 and precedes 822. As a prime number, 821 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 821. 821 is classified as a deficient number based on the sum of its proper divisors. In computer science, 821 is represented as 1100110101 in binary and 335 in hexadecimal. Historically, it is written as DCCCXXI in Roman numerals.
Factor Analysis
2 FactorsProperties
821 is prime, so its only factors are 1 and 821.
Divisible by 2
821 ends in 1, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 21 are not divisible by 4.
Divisible by 5
821 does not end in 0 or 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
821 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Deficient classification and digit analytics place 821 within several notable number theory sequences:
Timeline
Deep dive
How 821 breaks down
821 carries 2 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100110101 supports bitwise reasoning, hexadecimal 335 aligns with computing notation, and the Roman numeral DCCCXXI keeps the encyclopedic tradition alive. These attributes make 821 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 821 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (816–826) to tune search ranges, and educators feature 821 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 821 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 821
Is 821 a prime number?
821 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 821?
821 is already prime, so the factorization is simply 821.
How is 821 represented in binary and hexadecimal?
821 converts to 1100110101 in binary and 335 in hexadecimal, which are helpful for computer science applications.
Is 821 a perfect square, cube, or triangular number?
821 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 821?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.