289
289 is a odd composite number that follows 288 and precedes 290. It is composed of 3 distinct factors: 1, 17, 289. Its prime factorization can be written as 17^2. 289 is classified as a deficient number based on the sum of its proper divisors. In computer science, 289 is represented as 100100001 in binary and 121 in hexadecimal. Historically, it is written as CCLXXXIX in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
3 FactorsProperties
The prime factorization (17^2) reveals 2 prime building blocks.
Divisible by 2
289 ends in 9, so it is odd.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 89 are not divisible by 4.
Divisible by 5
289 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 19 is not a multiple of 9.
Divisible by 10
289 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 289 within several notable number theory sequences:
Timeline
Deep dive
How 289 breaks down
289 carries 3 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 18, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100100001 supports bitwise reasoning, hexadecimal 121 aligns with computing notation, and the Roman numeral CCLXXXIX keeps the encyclopedic tradition alive. These attributes make 289 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 289 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (284–294) to tune search ranges, and educators feature 289 in worksheets about factor trees. Its binary footprint of length 9 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 289 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 289
Is 289 a prime number?
289 is composite with 3 total factors and the prime factorization 17^2.
What is the prime factorization of 289?
It breaks down as 17^2, multiplying the primes 17 × 17.
How is 289 represented in binary and hexadecimal?
289 converts to 100100001 in binary and 121 in hexadecimal, which are helpful for computer science applications.
Is 289 a perfect square, cube, or triangular number?
289 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 289?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.