828
828 is a even composite number that follows 827 and precedes 829. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. Its prime factorization can be written as 2^2 × 3^2 × 23. 828 is classified as a abundant number based on the sum of its proper divisors. In computer science, 828 is represented as 1100111100 in binary and 33C in hexadecimal. Historically, it is written as DCCCXXVIII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 23) reveals 5 prime building blocks.
Divisible by 2
828 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
828 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 18 is a multiple of 9.
Divisible by 10
828 does not end in 0.
Divisible by 11
The alternating digit sum 14 is not a multiple of 11.
Abundant classification and digit analytics place 828 within several notable number theory sequences:
Timeline
Deep dive
How 828 breaks down
828 carries 18 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1356, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100111100 supports bitwise reasoning, hexadecimal 33C aligns with computing notation, and the Roman numeral DCCCXXVIII keeps the encyclopedic tradition alive. These attributes make 828 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 828 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (823–833) to tune search ranges, and educators feature 828 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 828 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 828
Is 828 a prime number?
828 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 23.
What is the prime factorization of 828?
It breaks down as 2^2 × 3^2 × 23, multiplying the primes 2 × 2 × 3 × 3 × 23.
How is 828 represented in binary and hexadecimal?
828 converts to 1100111100 in binary and 33C in hexadecimal, which are helpful for computer science applications.
Is 828 a perfect square, cube, or triangular number?
828 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 828?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.