2689
2689 is a odd prime number that follows 2688 and precedes 2690. As a prime number, 2689 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 2689. 2689 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2689 is represented as 101010000001 in binary and A81 in hexadecimal. Historically, it is written as MMDCLXXXIX in Roman numerals.
Factor Analysis
2 FactorsProperties
2689 is prime, so its only factors are 1 and 2689.
Divisible by 2
2689 ends in 9, so it is odd.
Divisible by 3
The digit sum 25 is not a multiple of 3.
Divisible by 4
The last two digits 89 are not divisible by 4.
Divisible by 5
2689 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 25 is not a multiple of 9.
Divisible by 10
2689 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 2689 within several notable number theory sequences:
Timeline
Deep dive
How 2689 breaks down
2689 carries 2 distinct factors and a digit signature of 25 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010000001 supports bitwise reasoning, hexadecimal A81 aligns with computing notation, and the Roman numeral MMDCLXXXIX keeps the encyclopedic tradition alive. These attributes make 2689 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2689 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2684–2694) to tune search ranges, and educators feature 2689 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 2689 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 2689
Is 2689 a prime number?
2689 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 2689?
2689 is already prime, so the factorization is simply 2689.
How is 2689 represented in binary and hexadecimal?
2689 converts to 101010000001 in binary and A81 in hexadecimal, which are helpful for computer science applications.
Is 2689 a perfect square, cube, or triangular number?
2689 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2689?
The digits sum to 25, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.