2208
2208 is a even composite number that follows 2207 and precedes 2209. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208. Its prime factorization can be written as 2^5 × 3 × 23. 2208 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2208 is represented as 100010100000 in binary and 8A0 in hexadecimal. Historically, it is written as MMCCVIII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 3 × 23) reveals 7 prime building blocks.
Divisible by 2
2208 ends in 8, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
2208 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 12 is not a multiple of 9.
Divisible by 10
2208 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Abundant classification and digit analytics place 2208 within several notable number theory sequences:
Timeline
Deep dive
How 2208 breaks down
2208 carries 24 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 3840, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100010100000 supports bitwise reasoning, hexadecimal 8A0 aligns with computing notation, and the Roman numeral MMCCVIII keeps the encyclopedic tradition alive. These attributes make 2208 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2208 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2203–2213) to tune search ranges, and educators feature 2208 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, Abundant numbers) help historians, numerologists, and trivia writers tie 2208 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 2208
Is 2208 a prime number?
2208 is composite with 24 total factors and the prime factorization 2^5 × 3 × 23.
What is the prime factorization of 2208?
It breaks down as 2^5 × 3 × 23, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 23.
How is 2208 represented in binary and hexadecimal?
2208 converts to 100010100000 in binary and 8A0 in hexadecimal, which are helpful for computer science applications.
Is 2208 a perfect square, cube, or triangular number?
2208 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2208?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.