816
816 is a even composite number that follows 815 and precedes 817. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816. Its prime factorization can be written as 2^4 × 3 × 17. 816 is classified as a abundant number based on the sum of its proper divisors. In computer science, 816 is represented as 1100110000 in binary and 330 in hexadecimal. Historically, it is written as DCCCXVI in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 17) reveals 6 prime building blocks.
Divisible by 2
816 ends in 6, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
816 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 15 is not a multiple of 9.
Divisible by 10
816 does not end in 0.
Divisible by 11
The alternating digit sum 13 is not a multiple of 11.
Abundant classification and digit analytics place 816 within several notable number theory sequences:
Timeline
Deep dive
How 816 breaks down
816 carries 20 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 1416, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100110000 supports bitwise reasoning, hexadecimal 330 aligns with computing notation, and the Roman numeral DCCCXVI keeps the encyclopedic tradition alive. These attributes make 816 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 816 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (811–821) to tune search ranges, and educators feature 816 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, Abundant numbers) help historians, numerologists, and trivia writers tie 816 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 816
Is 816 a prime number?
816 is composite with 20 total factors and the prime factorization 2^4 × 3 × 17.
What is the prime factorization of 816?
It breaks down as 2^4 × 3 × 17, multiplying the primes 2 × 2 × 2 × 2 × 3 × 17.
How is 816 represented in binary and hexadecimal?
816 converts to 1100110000 in binary and 330 in hexadecimal, which are helpful for computer science applications.
Is 816 a perfect square, cube, or triangular number?
816 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 816?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.