8289
8289 is a odd composite number that follows 8288 and precedes 8290. It is composed of 8 distinct factors: 1, 3, 9, 27, 307, 921, 2763, 8289. Its prime factorization can be written as 3^3 × 307. 8289 is classified as a deficient number based on the sum of its proper divisors. In computer science, 8289 is represented as 10000001100001 in binary and 2061 in hexadecimal.
Factor Analysis
8 FactorsProperties
The prime factorization (3^3 × 307) reveals 4 prime building blocks.
Divisible by 2
8289 ends in 9, so it is odd.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 89 are not divisible by 4.
Divisible by 5
8289 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 27 is a multiple of 9.
Divisible by 10
8289 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 8289 within several notable number theory sequences:
Timeline
Deep dive
How 8289 breaks down
8289 carries 8 distinct factors and a digit signature of 27 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 4031, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000001100001 supports bitwise reasoning, hexadecimal 2061 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8289 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8289 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8284–8294) to tune search ranges, and educators feature 8289 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 8289 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 8289
Is 8289 a prime number?
8289 is composite with 8 total factors and the prime factorization 3^3 × 307.
What is the prime factorization of 8289?
It breaks down as 3^3 × 307, multiplying the primes 3 × 3 × 3 × 307.
How is 8289 represented in binary and hexadecimal?
8289 converts to 10000001100001 in binary and 2061 in hexadecimal, which are helpful for computer science applications.
Is 8289 a perfect square, cube, or triangular number?
8289 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8289?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.