3204
3204 is a even composite number that follows 3203 and precedes 3205. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 36, 89, 178, 267, 356, 534, 801, 1068, 1602, 3204. Its prime factorization can be written as 2^2 × 3^2 × 89. 3204 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3204 is represented as 110010000100 in binary and C84 in hexadecimal. Historically, it is written as MMMCCIV in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 89) reveals 5 prime building blocks.
Divisible by 2
3204 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
3204 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 9 is a multiple of 9.
Divisible by 10
3204 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 3204 within several notable number theory sequences:
Timeline
Deep dive
How 3204 breaks down
3204 carries 18 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4986, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010000100 supports bitwise reasoning, hexadecimal C84 aligns with computing notation, and the Roman numeral MMMCCIV keeps the encyclopedic tradition alive. These attributes make 3204 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3204 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3199–3209) to tune search ranges, and educators feature 3204 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 3204 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 3204
Is 3204 a prime number?
3204 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 89.
What is the prime factorization of 3204?
It breaks down as 2^2 × 3^2 × 89, multiplying the primes 2 × 2 × 3 × 3 × 89.
How is 3204 represented in binary and hexadecimal?
3204 converts to 110010000100 in binary and C84 in hexadecimal, which are helpful for computer science applications.
Is 3204 a perfect square, cube, or triangular number?
3204 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3204?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.