827
827 is a odd prime number that follows 826 and precedes 828. As a prime number, 827 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 827. 827 is classified as a deficient number based on the sum of its proper divisors. In computer science, 827 is represented as 1100111011 in binary and 33B in hexadecimal. Historically, it is written as DCCCXXVII in Roman numerals.
Factor Analysis
2 FactorsProperties
827 is prime, so its only factors are 1 and 827.
Divisible by 2
827 ends in 7, so it is odd.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 27 are not divisible by 4.
Divisible by 5
827 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 17 is not a multiple of 9.
Divisible by 10
827 does not end in 0.
Divisible by 11
The alternating digit sum 13 is not a multiple of 11.
Deficient classification and digit analytics place 827 within several notable number theory sequences:
Timeline
Deep dive
How 827 breaks down
827 carries 2 distinct factors and a digit signature of 17 (8 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 1100111011 supports bitwise reasoning, hexadecimal 33B aligns with computing notation, and the Roman numeral DCCCXXVII keeps the encyclopedic tradition alive. These attributes make 827 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 827 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (822–832) to tune search ranges, and educators feature 827 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 827 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 827
Is 827 a prime number?
827 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 827?
827 is already prime, so the factorization is simply 827.
How is 827 represented in binary and hexadecimal?
827 converts to 1100111011 in binary and 33B in hexadecimal, which are helpful for computer science applications.
Is 827 a perfect square, cube, or triangular number?
827 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 827?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.