7688
7688 is a even composite number that follows 7687 and precedes 7689. It is composed of 12 distinct factors: 1, 2, 4, 8, 31, 62, 124, 248, 961, 1922, 3844, 7688. Its prime factorization can be written as 2^3 × 31^2. 7688 is classified as a deficient number based on the sum of its proper divisors. In computer science, 7688 is represented as 1111000001000 in binary and 1E08 in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2^3 × 31^2) reveals 5 prime building blocks.
Divisible by 2
7688 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 88 form a multiple of 4.
Divisible by 5
7688 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
7688 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 7688 within several notable number theory sequences:
Timeline
Deep dive
How 7688 breaks down
7688 carries 12 distinct factors and a digit signature of 29 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 7207, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111000001000 supports bitwise reasoning, hexadecimal 1E08 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7688 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7688 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7683–7693) to tune search ranges, and educators feature 7688 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, Deficient numbers) help historians, numerologists, and trivia writers tie 7688 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 7688
Is 7688 a prime number?
7688 is composite with 12 total factors and the prime factorization 2^3 × 31^2.
What is the prime factorization of 7688?
It breaks down as 2^3 × 31^2, multiplying the primes 2 × 2 × 2 × 31 × 31.
How is 7688 represented in binary and hexadecimal?
7688 converts to 1111000001000 in binary and 1E08 in hexadecimal, which are helpful for computer science applications.
Is 7688 a perfect square, cube, or triangular number?
7688 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7688?
The digits sum to 29, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.