8320
8320 is a even composite number that follows 8319 and precedes 8321. It is composed of 32 distinct factors: 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 64, 65, 80, 104, 128, 130, 160, 208, 260, 320, 416, 520, 640, 832, 1040, 1664, 2080, 4160, 8320. Its prime factorization can be written as 2^7 × 5 × 13. 8320 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8320 is represented as 10000010000000 in binary and 2080 in hexadecimal.
Factor Analysis
32 FactorsProperties
The prime factorization (2^7 × 5 × 13) reveals 9 prime building blocks.
Divisible by 2
8320 ends in 0, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
8320 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 13 is not a multiple of 9.
Divisible by 10
8320 ends in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 8320 within several notable number theory sequences:
Timeline
Deep dive
How 8320 breaks down
8320 carries 32 distinct factors and a digit signature of 13 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 13100, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000010000000 supports bitwise reasoning, hexadecimal 2080 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8320 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8320 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8315–8325) to tune search ranges, and educators feature 8320 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, Abundant numbers) help historians, numerologists, and trivia writers tie 8320 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 8320
Is 8320 a prime number?
8320 is composite with 32 total factors and the prime factorization 2^7 × 5 × 13.
What is the prime factorization of 8320?
It breaks down as 2^7 × 5 × 13, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 13.
How is 8320 represented in binary and hexadecimal?
8320 converts to 10000010000000 in binary and 2080 in hexadecimal, which are helpful for computer science applications.
Is 8320 a perfect square, cube, or triangular number?
8320 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8320?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.