208
208 is a even composite number that follows 207 and precedes 209. It is composed of 10 distinct factors: 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. Its prime factorization can be written as 2^4 × 13. 208 is classified as a abundant number based on the sum of its proper divisors. In computer science, 208 is represented as 11010000 in binary and D0 in hexadecimal. Historically, it is written as CCVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 13) reveals 5 prime building blocks.
Divisible by 2
208 ends in 8, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
208 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 10 is not a multiple of 9.
Divisible by 10
208 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 208 within several notable number theory sequences:
Timeline
Deep dive
How 208 breaks down
208 carries 10 distinct factors and a digit signature of 10 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 226, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010000 supports bitwise reasoning, hexadecimal D0 aligns with computing notation, and the Roman numeral CCVIII keeps the encyclopedic tradition alive. These attributes make 208 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 208 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (203–213) to tune search ranges, and educators feature 208 in worksheets about factor trees. Its binary footprint of length 8 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 208 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 208
Is 208 a prime number?
208 is composite with 10 total factors and the prime factorization 2^4 × 13.
What is the prime factorization of 208?
It breaks down as 2^4 × 13, multiplying the primes 2 × 2 × 2 × 2 × 13.
How is 208 represented in binary and hexadecimal?
208 converts to 11010000 in binary and D0 in hexadecimal, which are helpful for computer science applications.
Is 208 a perfect square, cube, or triangular number?
208 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 208?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.