2563
2563 is a odd composite number that follows 2562 and precedes 2564. It is composed of 4 distinct factors: 1, 11, 233, 2563. Its prime factorization can be written as 11 × 233. 2563 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2563 is represented as 101000000011 in binary and A03 in hexadecimal. Historically, it is written as MMDLXIII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (11 × 233) reveals 2 prime building blocks.
Divisible by 2
2563 ends in 3, so it is odd.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 63 are not divisible by 4.
Divisible by 5
2563 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 16 is not a multiple of 9.
Divisible by 10
2563 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 2563 within several notable number theory sequences:
Timeline
Deep dive
How 2563 breaks down
2563 carries 4 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 245, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101000000011 supports bitwise reasoning, hexadecimal A03 aligns with computing notation, and the Roman numeral MMDLXIII keeps the encyclopedic tradition alive. These attributes make 2563 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2563 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2558–2568) to tune search ranges, and educators feature 2563 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 2563 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 2563
Is 2563 a prime number?
2563 is composite with 4 total factors and the prime factorization 11 × 233.
What is the prime factorization of 2563?
It breaks down as 11 × 233, multiplying the primes 11 × 233.
How is 2563 represented in binary and hexadecimal?
2563 converts to 101000000011 in binary and A03 in hexadecimal, which are helpful for computer science applications.
Is 2563 a perfect square, cube, or triangular number?
2563 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2563?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.