689
689 is a odd composite number that follows 688 and precedes 690. It is composed of 4 distinct factors: 1, 13, 53, 689. Its prime factorization can be written as 13 × 53. 689 is classified as a deficient number based on the sum of its proper divisors. In computer science, 689 is represented as 1010110001 in binary and 2B1 in hexadecimal. Historically, it is written as DCLXXXIX in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (13 × 53) reveals 2 prime building blocks.
Divisible by 2
689 ends in 9, so it is odd.
Divisible by 3
The digit sum 23 is not a multiple of 3.
Divisible by 4
The last two digits 89 are not divisible by 4.
Divisible by 5
689 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
689 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 689 within several notable number theory sequences:
Timeline
Deep dive
How 689 breaks down
689 carries 4 distinct factors and a digit signature of 23 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 67, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010110001 supports bitwise reasoning, hexadecimal 2B1 aligns with computing notation, and the Roman numeral DCLXXXIX keeps the encyclopedic tradition alive. These attributes make 689 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 689 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (684–694) to tune search ranges, and educators feature 689 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 689 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 689
Is 689 a prime number?
689 is composite with 4 total factors and the prime factorization 13 × 53.
What is the prime factorization of 689?
It breaks down as 13 × 53, multiplying the primes 13 × 53.
How is 689 represented in binary and hexadecimal?
689 converts to 1010110001 in binary and 2B1 in hexadecimal, which are helpful for computer science applications.
Is 689 a perfect square, cube, or triangular number?
689 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 689?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.