814
814 is a even composite number that follows 813 and precedes 815. It is composed of 8 distinct factors: 1, 2, 11, 22, 37, 74, 407, 814. Its prime factorization can be written as 2 × 11 × 37. 814 is classified as a deficient number based on the sum of its proper divisors. In computer science, 814 is represented as 1100101110 in binary and 32E in hexadecimal. Historically, it is written as DCCCXIV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 11 × 37) reveals 3 prime building blocks.
Divisible by 2
814 ends in 4, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 14 are not divisible by 4.
Divisible by 5
814 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
814 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Deficient classification and digit analytics place 814 within several notable number theory sequences:
Timeline
Deep dive
How 814 breaks down
814 carries 8 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 554, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100101110 supports bitwise reasoning, hexadecimal 32E aligns with computing notation, and the Roman numeral DCCCXIV keeps the encyclopedic tradition alive. These attributes make 814 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 814 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (809–819) to tune search ranges, and educators feature 814 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 814 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 814
Is 814 a prime number?
814 is composite with 8 total factors and the prime factorization 2 × 11 × 37.
What is the prime factorization of 814?
It breaks down as 2 × 11 × 37, multiplying the primes 2 × 11 × 37.
How is 814 represented in binary and hexadecimal?
814 converts to 1100101110 in binary and 32E in hexadecimal, which are helpful for computer science applications.
Is 814 a perfect square, cube, or triangular number?
814 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 814?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.