8192
8192 is a even composite number that follows 8191 and precedes 8193. It is composed of 14 distinct factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192. Its prime factorization can be written as 2^13. 8192 is classified as a deficient number based on the sum of its proper divisors. In computer science, 8192 is represented as 10000000000000 in binary and 2000 in hexadecimal.
Factor Analysis
14 FactorsProperties
The prime factorization (2^13) reveals 13 prime building blocks.
Divisible by 2
8192 ends in 2, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
8192 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 20 is not a multiple of 9.
Divisible by 10
8192 does not end in 0.
Divisible by 11
The alternating digit sum 14 is not a multiple of 11.
Deficient classification and digit analytics place 8192 within several notable number theory sequences:
Timeline
Deep dive
How 8192 breaks down
8192 carries 14 distinct factors and a digit signature of 20 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 8191, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000000000 supports bitwise reasoning, hexadecimal 2000 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8192 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8192 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8187–8197) to tune search ranges, and educators feature 8192 in worksheets about factor trees. Its binary footprint of length 14 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 8192 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 8192
Is 8192 a prime number?
8192 is composite with 14 total factors and the prime factorization 2^13.
What is the prime factorization of 8192?
It breaks down as 2^13, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
How is 8192 represented in binary and hexadecimal?
8192 converts to 10000000000000 in binary and 2000 in hexadecimal, which are helpful for computer science applications.
Is 8192 a perfect square, cube, or triangular number?
8192 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8192?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.