768
768 is a even composite number that follows 767 and precedes 769. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768. Its prime factorization can be written as 2^8 × 3. 768 is classified as a abundant number based on the sum of its proper divisors. In computer science, 768 is represented as 1100000000 in binary and 300 in hexadecimal. Historically, it is written as DCCLXVIII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^8 × 3) reveals 9 prime building blocks.
Divisible by 2
768 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
768 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 21 is not a multiple of 9.
Divisible by 10
768 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 768 within several notable number theory sequences:
Timeline
Deep dive
How 768 breaks down
768 carries 18 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1276, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100000000 supports bitwise reasoning, hexadecimal 300 aligns with computing notation, and the Roman numeral DCCLXVIII keeps the encyclopedic tradition alive. These attributes make 768 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 768 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (763–773) to tune search ranges, and educators feature 768 in worksheets about factor trees. Its binary footprint of length 10 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 768 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 768
Is 768 a prime number?
768 is composite with 18 total factors and the prime factorization 2^8 × 3.
What is the prime factorization of 768?
It breaks down as 2^8 × 3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.
How is 768 represented in binary and hexadecimal?
768 converts to 1100000000 in binary and 300 in hexadecimal, which are helpful for computer science applications.
Is 768 a perfect square, cube, or triangular number?
768 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 768?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.