822
822 is a even composite number that follows 821 and precedes 823. It is composed of 8 distinct factors: 1, 2, 3, 6, 137, 274, 411, 822. Its prime factorization can be written as 2 × 3 × 137. 822 is classified as a abundant number based on the sum of its proper divisors. In computer science, 822 is represented as 1100110110 in binary and 336 in hexadecimal. Historically, it is written as DCCCXXII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 137) reveals 3 prime building blocks.
Divisible by 2
822 ends in 2, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 22 are not divisible by 4.
Divisible by 5
822 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 12 is not a multiple of 9.
Divisible by 10
822 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 822 within several notable number theory sequences:
Timeline
Deep dive
How 822 breaks down
822 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 834, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100110110 supports bitwise reasoning, hexadecimal 336 aligns with computing notation, and the Roman numeral DCCCXXII keeps the encyclopedic tradition alive. These attributes make 822 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 822 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (817–827) to tune search ranges, and educators feature 822 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 822 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 822
Is 822 a prime number?
822 is composite with 8 total factors and the prime factorization 2 × 3 × 137.
What is the prime factorization of 822?
It breaks down as 2 × 3 × 137, multiplying the primes 2 × 3 × 137.
How is 822 represented in binary and hexadecimal?
822 converts to 1100110110 in binary and 336 in hexadecimal, which are helpful for computer science applications.
Is 822 a perfect square, cube, or triangular number?
822 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 822?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.