1791
1791 is a odd composite number that follows 1790 and precedes 1792. It is composed of 6 distinct factors: 1, 3, 9, 199, 597, 1791. Its prime factorization can be written as 3^2 × 199. 1791 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1791 is represented as 11011111111 in binary and 6FF in hexadecimal. Historically, it is written as MDCCXCI in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3^2 × 199) reveals 3 prime building blocks.
Divisible by 2
1791 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
1791 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
1791 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 1791 within several notable number theory sequences:
Timeline
Deep dive
How 1791 breaks down
1791 carries 6 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 809, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011111111 supports bitwise reasoning, hexadecimal 6FF aligns with computing notation, and the Roman numeral MDCCXCI keeps the encyclopedic tradition alive. These attributes make 1791 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1791 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1786–1796) to tune search ranges, and educators feature 1791 in worksheets about factor trees. Its binary footprint of length 11 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 1791 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 1791
Is 1791 a prime number?
1791 is composite with 6 total factors and the prime factorization 3^2 × 199.
What is the prime factorization of 1791?
It breaks down as 3^2 × 199, multiplying the primes 3 × 3 × 199.
How is 1791 represented in binary and hexadecimal?
1791 converts to 11011111111 in binary and 6FF in hexadecimal, which are helpful for computer science applications.
Is 1791 a perfect square, cube, or triangular number?
1791 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1791?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.