2264
2264 is a even composite number that follows 2263 and precedes 2265. It is composed of 8 distinct factors: 1, 2, 4, 8, 283, 566, 1132, 2264. Its prime factorization can be written as 2^3 × 283. 2264 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2264 is represented as 100011011000 in binary and 8D8 in hexadecimal. Historically, it is written as MMCCLXIV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 283) reveals 4 prime building blocks.
Divisible by 2
2264 ends in 4, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
2264 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
2264 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 2264 within several notable number theory sequences:
Timeline
Deep dive
How 2264 breaks down
2264 carries 8 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1996, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100011011000 supports bitwise reasoning, hexadecimal 8D8 aligns with computing notation, and the Roman numeral MMCCLXIV keeps the encyclopedic tradition alive. These attributes make 2264 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2264 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2259–2269) to tune search ranges, and educators feature 2264 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 2264 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 2264
Is 2264 a prime number?
2264 is composite with 8 total factors and the prime factorization 2^3 × 283.
What is the prime factorization of 2264?
It breaks down as 2^3 × 283, multiplying the primes 2 × 2 × 2 × 283.
How is 2264 represented in binary and hexadecimal?
2264 converts to 100011011000 in binary and 8D8 in hexadecimal, which are helpful for computer science applications.
Is 2264 a perfect square, cube, or triangular number?
2264 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2264?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.