6768
6768 is a even composite number that follows 6767 and precedes 6769. It is composed of 30 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 47, 48, 72, 94, 141, 144, 188, 282, 376, 423, 564, 752, 846, 1128, 1692, 2256, 3384, 6768. Its prime factorization can be written as 2^4 × 3^2 × 47. 6768 is classified as a abundant number based on the sum of its proper divisors. In computer science, 6768 is represented as 1101001110000 in binary and 1A70 in hexadecimal.
Factor Analysis
30 FactorsProperties
The prime factorization (2^4 × 3^2 × 47) reveals 7 prime building blocks.
Divisible by 2
6768 ends in 8, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
6768 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 27 is a multiple of 9.
Divisible by 10
6768 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 6768 within several notable number theory sequences:
Timeline
Deep dive
How 6768 breaks down
6768 carries 30 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 12576, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101001110000 supports bitwise reasoning, hexadecimal 1A70 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 6768 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 6768 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (6763–6773) to tune search ranges, and educators feature 6768 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 6768 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 6768
Is 6768 a prime number?
6768 is composite with 30 total factors and the prime factorization 2^4 × 3^2 × 47.
What is the prime factorization of 6768?
It breaks down as 2^4 × 3^2 × 47, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 47.
How is 6768 represented in binary and hexadecimal?
6768 converts to 1101001110000 in binary and 1A70 in hexadecimal, which are helpful for computer science applications.
Is 6768 a perfect square, cube, or triangular number?
6768 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 6768?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.