2313
2313 is a odd composite number that follows 2312 and precedes 2314. It is composed of 6 distinct factors: 1, 3, 9, 257, 771, 2313. Its prime factorization can be written as 3^2 × 257. 2313 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2313 is represented as 100100001001 in binary and 909 in hexadecimal. Historically, it is written as MMCCCXIII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3^2 × 257) reveals 3 prime building blocks.
Divisible by 2
2313 ends in 3, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
2313 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 9 is a multiple of 9.
Divisible by 10
2313 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 2313 within several notable number theory sequences:
Timeline
Deep dive
How 2313 breaks down
2313 carries 6 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 1041, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100100001001 supports bitwise reasoning, hexadecimal 909 aligns with computing notation, and the Roman numeral MMCCCXIII keeps the encyclopedic tradition alive. These attributes make 2313 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2313 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2308–2318) to tune search ranges, and educators feature 2313 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 2313 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 2313
Is 2313 a prime number?
2313 is composite with 6 total factors and the prime factorization 3^2 × 257.
What is the prime factorization of 2313?
It breaks down as 3^2 × 257, multiplying the primes 3 × 3 × 257.
How is 2313 represented in binary and hexadecimal?
2313 converts to 100100001001 in binary and 909 in hexadecimal, which are helpful for computer science applications.
Is 2313 a perfect square, cube, or triangular number?
2313 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2313?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.