2768
2768 is a even composite number that follows 2767 and precedes 2769. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 173, 346, 692, 1384, 2768. Its prime factorization can be written as 2^4 × 173. 2768 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2768 is represented as 101011010000 in binary and AD0 in hexadecimal. Historically, it is written as MMDCCLXVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 173) reveals 5 prime building blocks.
Divisible by 2
2768 ends in 8, so it is even.
Divisible by 3
The digit sum 23 is not a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
2768 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 23 is not a multiple of 9.
Divisible by 10
2768 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Deficient classification and digit analytics place 2768 within several notable number theory sequences:
Timeline
Deep dive
How 2768 breaks down
2768 carries 10 distinct factors and a digit signature of 23 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 2626, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101011010000 supports bitwise reasoning, hexadecimal AD0 aligns with computing notation, and the Roman numeral MMDCCLXVIII keeps the encyclopedic tradition alive. These attributes make 2768 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2768 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2763–2773) to tune search ranges, and educators feature 2768 in worksheets about factor trees. Its binary footprint of length 12 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 2768 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 2768
Is 2768 a prime number?
2768 is composite with 10 total factors and the prime factorization 2^4 × 173.
What is the prime factorization of 2768?
It breaks down as 2^4 × 173, multiplying the primes 2 × 2 × 2 × 2 × 173.
How is 2768 represented in binary and hexadecimal?
2768 converts to 101011010000 in binary and AD0 in hexadecimal, which are helpful for computer science applications.
Is 2768 a perfect square, cube, or triangular number?
2768 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2768?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.