3201
3201 is a odd composite number that follows 3200 and precedes 3202. It is composed of 8 distinct factors: 1, 3, 11, 33, 97, 291, 1067, 3201. Its prime factorization can be written as 3 × 11 × 97. 3201 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3201 is represented as 110010000001 in binary and C81 in hexadecimal. Historically, it is written as MMMCCI in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 11 × 97) reveals 3 prime building blocks.
Divisible by 2
3201 ends in 1, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
3201 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 6 is not a multiple of 9.
Divisible by 10
3201 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 3201 within several notable number theory sequences:
Timeline
Deep dive
How 3201 breaks down
3201 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 1503, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010000001 supports bitwise reasoning, hexadecimal C81 aligns with computing notation, and the Roman numeral MMMCCI keeps the encyclopedic tradition alive. These attributes make 3201 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3201 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3196–3206) to tune search ranges, and educators feature 3201 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 3201 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 3201
Is 3201 a prime number?
3201 is composite with 8 total factors and the prime factorization 3 × 11 × 97.
What is the prime factorization of 3201?
It breaks down as 3 × 11 × 97, multiplying the primes 3 × 11 × 97.
How is 3201 represented in binary and hexadecimal?
3201 converts to 110010000001 in binary and C81 in hexadecimal, which are helpful for computer science applications.
Is 3201 a perfect square, cube, or triangular number?
3201 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3201?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.