688
688 is a even composite number that follows 687 and precedes 689. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 43, 86, 172, 344, 688. Its prime factorization can be written as 2^4 × 43. 688 is classified as a deficient number based on the sum of its proper divisors. In computer science, 688 is represented as 1010110000 in binary and 2B0 in hexadecimal. Historically, it is written as DCLXXXVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 43) reveals 5 prime building blocks.
Divisible by 2
688 ends in 8, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
688 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 22 is not a multiple of 9.
Divisible by 10
688 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Deficient classification and digit analytics place 688 within several notable number theory sequences:
Timeline
Deep dive
How 688 breaks down
688 carries 10 distinct factors and a digit signature of 22 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 676, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010110000 supports bitwise reasoning, hexadecimal 2B0 aligns with computing notation, and the Roman numeral DCLXXXVIII keeps the encyclopedic tradition alive. These attributes make 688 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 688 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (683–693) to tune search ranges, and educators feature 688 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, Deficient numbers) help historians, numerologists, and trivia writers tie 688 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 688
Is 688 a prime number?
688 is composite with 10 total factors and the prime factorization 2^4 × 43.
What is the prime factorization of 688?
It breaks down as 2^4 × 43, multiplying the primes 2 × 2 × 2 × 2 × 43.
How is 688 represented in binary and hexadecimal?
688 converts to 1010110000 in binary and 2B0 in hexadecimal, which are helpful for computer science applications.
Is 688 a perfect square, cube, or triangular number?
688 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 688?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.