3208
3208 is a even composite number that follows 3207 and precedes 3209. It is composed of 8 distinct factors: 1, 2, 4, 8, 401, 802, 1604, 3208. Its prime factorization can be written as 2^3 × 401. 3208 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3208 is represented as 110010001000 in binary and C88 in hexadecimal. Historically, it is written as MMMCCVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 401) reveals 4 prime building blocks.
Divisible by 2
3208 ends in 8, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
3208 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 13 is not a multiple of 9.
Divisible by 10
3208 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Deficient classification and digit analytics place 3208 within several notable number theory sequences:
Timeline
Deep dive
How 3208 breaks down
3208 carries 8 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 2822, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010001000 supports bitwise reasoning, hexadecimal C88 aligns with computing notation, and the Roman numeral MMMCCVIII keeps the encyclopedic tradition alive. These attributes make 3208 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3208 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3203–3213) to tune search ranges, and educators feature 3208 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 3208 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 3208
Is 3208 a prime number?
3208 is composite with 8 total factors and the prime factorization 2^3 × 401.
What is the prime factorization of 3208?
It breaks down as 2^3 × 401, multiplying the primes 2 × 2 × 2 × 401.
How is 3208 represented in binary and hexadecimal?
3208 converts to 110010001000 in binary and C88 in hexadecimal, which are helpful for computer science applications.
Is 3208 a perfect square, cube, or triangular number?
3208 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3208?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.