813
813 is a odd composite number that follows 812 and precedes 814. It is composed of 4 distinct factors: 1, 3, 271, 813. Its prime factorization can be written as 3 × 271. 813 is classified as a deficient number based on the sum of its proper divisors. In computer science, 813 is represented as 1100101101 in binary and 32D in hexadecimal. Historically, it is written as DCCCXIII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 271) reveals 2 prime building blocks.
Divisible by 2
813 ends in 3, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
813 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 12 is not a multiple of 9.
Divisible by 10
813 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Deficient classification and digit analytics place 813 within several notable number theory sequences:
Timeline
Deep dive
How 813 breaks down
813 carries 4 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 275, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100101101 supports bitwise reasoning, hexadecimal 32D aligns with computing notation, and the Roman numeral DCCCXIII keeps the encyclopedic tradition alive. These attributes make 813 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 813 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (808–818) to tune search ranges, and educators feature 813 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, Deficient numbers) help historians, numerologists, and trivia writers tie 813 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 813
Is 813 a prime number?
813 is composite with 4 total factors and the prime factorization 3 × 271.
What is the prime factorization of 813?
It breaks down as 3 × 271, multiplying the primes 3 × 271.
How is 813 represented in binary and hexadecimal?
813 converts to 1100101101 in binary and 32D in hexadecimal, which are helpful for computer science applications.
Is 813 a perfect square, cube, or triangular number?
813 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 813?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.