1688
1688 is a even composite number that follows 1687 and precedes 1689. It is composed of 8 distinct factors: 1, 2, 4, 8, 211, 422, 844, 1688. Its prime factorization can be written as 2^3 × 211. 1688 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1688 is represented as 11010011000 in binary and 698 in hexadecimal. Historically, it is written as MDCLXXXVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 211) reveals 4 prime building blocks.
Divisible by 2
1688 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 88 form a multiple of 4.
Divisible by 5
1688 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
1688 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Deficient classification and digit analytics place 1688 within several notable number theory sequences:
Timeline
Deep dive
How 1688 breaks down
1688 carries 8 distinct factors and a digit signature of 23 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1492, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010011000 supports bitwise reasoning, hexadecimal 698 aligns with computing notation, and the Roman numeral MDCLXXXVIII keeps the encyclopedic tradition alive. These attributes make 1688 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1688 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1683–1693) to tune search ranges, and educators feature 1688 in worksheets about factor trees. Its binary footprint of length 11 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 1688 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 1688
Is 1688 a prime number?
1688 is composite with 8 total factors and the prime factorization 2^3 × 211.
What is the prime factorization of 1688?
It breaks down as 2^3 × 211, multiplying the primes 2 × 2 × 2 × 211.
How is 1688 represented in binary and hexadecimal?
1688 converts to 11010011000 in binary and 698 in hexadecimal, which are helpful for computer science applications.
Is 1688 a perfect square, cube, or triangular number?
1688 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1688?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.