841
841 is a odd composite number that follows 840 and precedes 842. It is composed of 3 distinct factors: 1, 29, 841. Its prime factorization can be written as 29^2. 841 is classified as a deficient number based on the sum of its proper divisors. In computer science, 841 is represented as 1101001001 in binary and 349 in hexadecimal. Historically, it is written as DCCCXLI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
3 FactorsProperties
The prime factorization (29^2) reveals 2 prime building blocks.
Divisible by 2
841 ends in 1, so it is odd.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 41 are not divisible by 4.
Divisible by 5
841 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
841 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 841 within several notable number theory sequences:
Timeline
Deep dive
How 841 breaks down
841 carries 3 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 30, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101001001 supports bitwise reasoning, hexadecimal 349 aligns with computing notation, and the Roman numeral DCCCXLI keeps the encyclopedic tradition alive. These attributes make 841 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 841 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (836–846) to tune search ranges, and educators feature 841 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, Perfect squares) help historians, numerologists, and trivia writers tie 841 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 841
Is 841 a prime number?
841 is composite with 3 total factors and the prime factorization 29^2.
What is the prime factorization of 841?
It breaks down as 29^2, multiplying the primes 29 × 29.
How is 841 represented in binary and hexadecimal?
841 converts to 1101001001 in binary and 349 in hexadecimal, which are helpful for computer science applications.
Is 841 a perfect square, cube, or triangular number?
841 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 841?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.