7680
7680 is a even composite number that follows 7679 and precedes 7681. It is composed of 40 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536, 1920, 2560, 3840, 7680. Its prime factorization can be written as 2^9 × 3 × 5. 7680 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7680 is represented as 1111000000000 in binary and 1E00 in hexadecimal.
Factor Analysis
40 FactorsProperties
The prime factorization (2^9 × 3 × 5) reveals 11 prime building blocks.
Divisible by 2
7680 ends in 0, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
7680 ends in 0, so it is divisible by 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 21 is not a multiple of 9.
Divisible by 10
7680 ends in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 7680 within several notable number theory sequences:
Timeline
Deep dive
How 7680 breaks down
7680 carries 40 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 16872, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111000000000 supports bitwise reasoning, hexadecimal 1E00 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7680 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7680 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7675–7685) to tune search ranges, and educators feature 7680 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 7680 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 7680
Is 7680 a prime number?
7680 is composite with 40 total factors and the prime factorization 2^9 × 3 × 5.
What is the prime factorization of 7680?
It breaks down as 2^9 × 3 × 5, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5.
How is 7680 represented in binary and hexadecimal?
7680 converts to 1111000000000 in binary and 1E00 in hexadecimal, which are helpful for computer science applications.
Is 7680 a perfect square, cube, or triangular number?
7680 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7680?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.