8768
8768 is a even composite number that follows 8767 and precedes 8769. It is composed of 14 distinct factors: 1, 2, 4, 8, 16, 32, 64, 137, 274, 548, 1096, 2192, 4384, 8768. Its prime factorization can be written as 2^6 × 137. 8768 is classified as a deficient number based on the sum of its proper divisors. In computer science, 8768 is represented as 10001001000000 in binary and 2240 in hexadecimal.
Factor Analysis
14 FactorsProperties
The prime factorization (2^6 × 137) reveals 7 prime building blocks.
Divisible by 2
8768 ends in 8, so it is even.
Divisible by 3
The digit sum 29 is not a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
8768 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 29 is not a multiple of 9.
Divisible by 10
8768 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 8768 within several notable number theory sequences:
Timeline
Deep dive
How 8768 breaks down
8768 carries 14 distinct factors and a digit signature of 29 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 8758, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001001000000 supports bitwise reasoning, hexadecimal 2240 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8768 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8768 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8763–8773) to tune search ranges, and educators feature 8768 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 8768 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 8768
Is 8768 a prime number?
8768 is composite with 14 total factors and the prime factorization 2^6 × 137.
What is the prime factorization of 8768?
It breaks down as 2^6 × 137, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 137.
How is 8768 represented in binary and hexadecimal?
8768 converts to 10001001000000 in binary and 2240 in hexadecimal, which are helpful for computer science applications.
Is 8768 a perfect square, cube, or triangular number?
8768 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8768?
The digits sum to 29, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.