826
826 is a even composite number that follows 825 and precedes 827. It is composed of 8 distinct factors: 1, 2, 7, 14, 59, 118, 413, 826. Its prime factorization can be written as 2 × 7 × 59. 826 is classified as a deficient number based on the sum of its proper divisors. In computer science, 826 is represented as 1100111010 in binary and 33A in hexadecimal. Historically, it is written as DCCCXXVI in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 7 × 59) reveals 3 prime building blocks.
Divisible by 2
826 ends in 6, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 26 are not divisible by 4.
Divisible by 5
826 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 16 is not a multiple of 9.
Divisible by 10
826 does not end in 0.
Divisible by 11
The alternating digit sum 12 is not a multiple of 11.
Deficient classification and digit analytics place 826 within several notable number theory sequences:
Timeline
Deep dive
How 826 breaks down
826 carries 8 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 614, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100111010 supports bitwise reasoning, hexadecimal 33A aligns with computing notation, and the Roman numeral DCCCXXVI keeps the encyclopedic tradition alive. These attributes make 826 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 826 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (821–831) to tune search ranges, and educators feature 826 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 826 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 826
Is 826 a prime number?
826 is composite with 8 total factors and the prime factorization 2 × 7 × 59.
What is the prime factorization of 826?
It breaks down as 2 × 7 × 59, multiplying the primes 2 × 7 × 59.
How is 826 represented in binary and hexadecimal?
826 converts to 1100111010 in binary and 33A in hexadecimal, which are helpful for computer science applications.
Is 826 a perfect square, cube, or triangular number?
826 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 826?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.