891
891 is a odd composite number that follows 890 and precedes 892. It is composed of 10 distinct factors: 1, 3, 9, 11, 27, 33, 81, 99, 297, 891. Its prime factorization can be written as 3^4 × 11. 891 is classified as a deficient number based on the sum of its proper divisors. In computer science, 891 is represented as 1101111011 in binary and 37B in hexadecimal. Historically, it is written as DCCCXCI in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (3^4 × 11) reveals 5 prime building blocks.
Divisible by 2
891 ends in 1, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 91 are not divisible by 4.
Divisible by 5
891 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 18 is a multiple of 9.
Divisible by 10
891 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 891 within several notable number theory sequences:
Timeline
Deep dive
How 891 breaks down
891 carries 10 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 561, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101111011 supports bitwise reasoning, hexadecimal 37B aligns with computing notation, and the Roman numeral DCCCXCI keeps the encyclopedic tradition alive. These attributes make 891 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 891 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (886–896) to tune search ranges, and educators feature 891 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 891 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 891
Is 891 a prime number?
891 is composite with 10 total factors and the prime factorization 3^4 × 11.
What is the prime factorization of 891?
It breaks down as 3^4 × 11, multiplying the primes 3 × 3 × 3 × 3 × 11.
How is 891 represented in binary and hexadecimal?
891 converts to 1101111011 in binary and 37B in hexadecimal, which are helpful for computer science applications.
Is 891 a perfect square, cube, or triangular number?
891 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 891?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.