2561
2561 is a odd composite number that follows 2560 and precedes 2562. It is composed of 4 distinct factors: 1, 13, 197, 2561. Its prime factorization can be written as 13 × 197. 2561 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2561 is represented as 101000000001 in binary and A01 in hexadecimal. Historically, it is written as MMDLXI in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (13 × 197) reveals 2 prime building blocks.
Divisible by 2
2561 ends in 1, so it is odd.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 61 are not divisible by 4.
Divisible by 5
2561 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 14 is not a multiple of 9.
Divisible by 10
2561 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 2561 within several notable number theory sequences:
Timeline
Deep dive
How 2561 breaks down
2561 carries 4 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 211, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101000000001 supports bitwise reasoning, hexadecimal A01 aligns with computing notation, and the Roman numeral MMDLXI keeps the encyclopedic tradition alive. These attributes make 2561 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2561 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2556–2566) to tune search ranges, and educators feature 2561 in worksheets about factor trees. 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 (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 2561 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 2561
Is 2561 a prime number?
2561 is composite with 4 total factors and the prime factorization 13 × 197.
What is the prime factorization of 2561?
It breaks down as 13 × 197, multiplying the primes 13 × 197.
How is 2561 represented in binary and hexadecimal?
2561 converts to 101000000001 in binary and A01 in hexadecimal, which are helpful for computer science applications.
Is 2561 a perfect square, cube, or triangular number?
2561 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2561?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.