861
861 is a odd composite number that follows 860 and precedes 862. It is composed of 8 distinct factors: 1, 3, 7, 21, 41, 123, 287, 861. Its prime factorization can be written as 3 × 7 × 41. 861 is classified as a deficient number based on the sum of its proper divisors. In computer science, 861 is represented as 1101011101 in binary and 35D in hexadecimal. Historically, it is written as DCCCLXI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 7 × 41) reveals 3 prime building blocks.
Divisible by 2
861 ends in 1, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 61 are not divisible by 4.
Divisible by 5
861 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 15 is not a multiple of 9.
Divisible by 10
861 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 861 within several notable number theory sequences:
Timeline
Deep dive
How 861 breaks down
861 carries 8 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 483, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101011101 supports bitwise reasoning, hexadecimal 35D aligns with computing notation, and the Roman numeral DCCCLXI keeps the encyclopedic tradition alive. These attributes make 861 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 861 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (856–866) to tune search ranges, and educators feature 861 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, Triangular numbers) help historians, numerologists, and trivia writers tie 861 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 861
Is 861 a prime number?
861 is composite with 8 total factors and the prime factorization 3 × 7 × 41.
What is the prime factorization of 861?
It breaks down as 3 × 7 × 41, multiplying the primes 3 × 7 × 41.
How is 861 represented in binary and hexadecimal?
861 converts to 1101011101 in binary and 35D in hexadecimal, which are helpful for computer science applications.
Is 861 a perfect square, cube, or triangular number?
861 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 861?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.