1289
1289 is a odd prime number that follows 1288 and precedes 1290. As a prime number, 1289 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1289. 1289 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1289 is represented as 10100001001 in binary and 509 in hexadecimal. Historically, it is written as MCCLXXXIX in Roman numerals.
Factor Analysis
2 FactorsProperties
1289 is prime, so its only factors are 1 and 1289.
Divisible by 2
1289 ends in 9, so it is odd.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 89 are not divisible by 4.
Divisible by 5
1289 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 20 is not a multiple of 9.
Divisible by 10
1289 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Deficient classification and digit analytics place 1289 within several notable number theory sequences:
Timeline
Deep dive
How 1289 breaks down
1289 carries 2 distinct factors and a digit signature of 20 (2 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 10100001001 supports bitwise reasoning, hexadecimal 509 aligns with computing notation, and the Roman numeral MCCLXXXIX keeps the encyclopedic tradition alive. These attributes make 1289 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1289 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1284–1294) to tune search ranges, and educators feature 1289 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1289 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 1289
Is 1289 a prime number?
1289 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 1289?
1289 is already prime, so the factorization is simply 1289.
How is 1289 represented in binary and hexadecimal?
1289 converts to 10100001001 in binary and 509 in hexadecimal, which are helpful for computer science applications.
Is 1289 a perfect square, cube, or triangular number?
1289 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1289?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.