3684
3684 is a even composite number that follows 3683 and precedes 3685. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 307, 614, 921, 1228, 1842, 3684. Its prime factorization can be written as 2^2 × 3 × 307. 3684 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3684 is represented as 111001100100 in binary and E64 in hexadecimal. Historically, it is written as MMMDCLXXXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 307) reveals 4 prime building blocks.
Divisible by 2
3684 ends in 4, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
3684 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 21 is not a multiple of 9.
Divisible by 10
3684 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 3684 within several notable number theory sequences:
Timeline
Deep dive
How 3684 breaks down
3684 carries 12 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 4940, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001100100 supports bitwise reasoning, hexadecimal E64 aligns with computing notation, and the Roman numeral MMMDCLXXXIV keeps the encyclopedic tradition alive. These attributes make 3684 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3684 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3679–3689) to tune search ranges, and educators feature 3684 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 3684 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 3684
Is 3684 a prime number?
3684 is composite with 12 total factors and the prime factorization 2^2 × 3 × 307.
What is the prime factorization of 3684?
It breaks down as 2^2 × 3 × 307, multiplying the primes 2 × 2 × 3 × 307.
How is 3684 represented in binary and hexadecimal?
3684 converts to 111001100100 in binary and E64 in hexadecimal, which are helpful for computer science applications.
Is 3684 a perfect square, cube, or triangular number?
3684 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3684?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.