8064
8064 is a even composite number that follows 8063 and precedes 8065. It is composed of 48 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 384, 448, 504, 576, 672, 896, 1008, 1152, 1344, 2016, 2688, 4032, 8064. Its prime factorization can be written as 2^7 × 3^2 × 7. 8064 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8064 is represented as 1111110000000 in binary and 1F80 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^7 × 3^2 × 7) reveals 10 prime building blocks.
Divisible by 2
8064 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
8064 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
8064 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 8064 within several notable number theory sequences:
Timeline
Deep dive
How 8064 breaks down
8064 carries 48 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 18456, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111110000000 supports bitwise reasoning, hexadecimal 1F80 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8064 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8064 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8059–8069) to tune search ranges, and educators feature 8064 in worksheets about factor trees. Its binary footprint of length 13 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 8064 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 8064
Is 8064 a prime number?
8064 is composite with 48 total factors and the prime factorization 2^7 × 3^2 × 7.
What is the prime factorization of 8064?
It breaks down as 2^7 × 3^2 × 7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7.
How is 8064 represented in binary and hexadecimal?
8064 converts to 1111110000000 in binary and 1F80 in hexadecimal, which are helpful for computer science applications.
Is 8064 a perfect square, cube, or triangular number?
8064 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8064?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.