867
867 is a odd composite number that follows 866 and precedes 868. It is composed of 6 distinct factors: 1, 3, 17, 51, 289, 867. Its prime factorization can be written as 3 × 17^2. 867 is classified as a deficient number based on the sum of its proper divisors. In computer science, 867 is represented as 1101100011 in binary and 363 in hexadecimal. Historically, it is written as DCCCLXVII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3 × 17^2) reveals 3 prime building blocks.
Divisible by 2
867 ends in 7, so it is odd.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 67 are not divisible by 4.
Divisible by 5
867 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 21 is not a multiple of 9.
Divisible by 10
867 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Deficient classification and digit analytics place 867 within several notable number theory sequences:
Timeline
Deep dive
How 867 breaks down
867 carries 6 distinct factors and a digit signature of 21 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 361, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101100011 supports bitwise reasoning, hexadecimal 363 aligns with computing notation, and the Roman numeral DCCCLXVII keeps the encyclopedic tradition alive. These attributes make 867 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 867 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (862–872) to tune search ranges, and educators feature 867 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 867 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 867
Is 867 a prime number?
867 is composite with 6 total factors and the prime factorization 3 × 17^2.
What is the prime factorization of 867?
It breaks down as 3 × 17^2, multiplying the primes 3 × 17 × 17.
How is 867 represented in binary and hexadecimal?
867 converts to 1101100011 in binary and 363 in hexadecimal, which are helpful for computer science applications.
Is 867 a perfect square, cube, or triangular number?
867 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 867?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.