864
864 is a even composite number that follows 863 and precedes 865. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. Its prime factorization can be written as 2^5 × 3^3. 864 is classified as a abundant number based on the sum of its proper divisors. In computer science, 864 is represented as 1101100000 in binary and 360 in hexadecimal. Historically, it is written as DCCCLXIV in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 3^3) reveals 8 prime building blocks.
Divisible by 2
864 ends in 4, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
864 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
864 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 864 within several notable number theory sequences:
Timeline
Deep dive
How 864 breaks down
864 carries 24 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1656, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101100000 supports bitwise reasoning, hexadecimal 360 aligns with computing notation, and the Roman numeral DCCCLXIV keeps the encyclopedic tradition alive. These attributes make 864 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 864 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (859–869) to tune search ranges, and educators feature 864 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, Abundant numbers) help historians, numerologists, and trivia writers tie 864 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 864
Is 864 a prime number?
864 is composite with 24 total factors and the prime factorization 2^5 × 3^3.
What is the prime factorization of 864?
It breaks down as 2^5 × 3^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.
How is 864 represented in binary and hexadecimal?
864 converts to 1101100000 in binary and 360 in hexadecimal, which are helpful for computer science applications.
Is 864 a perfect square, cube, or triangular number?
864 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 864?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.