823
823 is a odd prime number that follows 822 and precedes 824. As a prime number, 823 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 823. 823 is classified as a deficient number based on the sum of its proper divisors. In computer science, 823 is represented as 1100110111 in binary and 337 in hexadecimal. Historically, it is written as DCCCXXIII in Roman numerals.
Factor Analysis
2 FactorsProperties
823 is prime, so its only factors are 1 and 823.
Divisible by 2
823 ends in 3, so it is odd.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 23 are not divisible by 4.
Divisible by 5
823 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 13 is not a multiple of 9.
Divisible by 10
823 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Deficient classification and digit analytics place 823 within several notable number theory sequences:
Timeline
Deep dive
How 823 breaks down
823 carries 2 distinct factors and a digit signature of 13 (4 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 1100110111 supports bitwise reasoning, hexadecimal 337 aligns with computing notation, and the Roman numeral DCCCXXIII keeps the encyclopedic tradition alive. These attributes make 823 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 823 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (818–828) to tune search ranges, and educators feature 823 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 823 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 823
Is 823 a prime number?
823 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 823?
823 is already prime, so the factorization is simply 823.
How is 823 represented in binary and hexadecimal?
823 converts to 1100110111 in binary and 337 in hexadecimal, which are helpful for computer science applications.
Is 823 a perfect square, cube, or triangular number?
823 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 823?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.