684
684 is a even composite number that follows 683 and precedes 685. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684. Its prime factorization can be written as 2^2 × 3^2 × 19. 684 is classified as a abundant number based on the sum of its proper divisors. In computer science, 684 is represented as 1010101100 in binary and 2AC in hexadecimal. Historically, it is written as DCLXXXIV in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 19) reveals 5 prime building blocks.
Divisible by 2
684 ends in 4, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
684 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 18 is a multiple of 9.
Divisible by 10
684 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 684 within several notable number theory sequences:
Timeline
Deep dive
How 684 breaks down
684 carries 18 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1136, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010101100 supports bitwise reasoning, hexadecimal 2AC aligns with computing notation, and the Roman numeral DCLXXXIV keeps the encyclopedic tradition alive. These attributes make 684 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 684 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (679–689) to tune search ranges, and educators feature 684 in worksheets about factor trees. Its binary footprint of length 10 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 684 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 684
Is 684 a prime number?
684 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 19.
What is the prime factorization of 684?
It breaks down as 2^2 × 3^2 × 19, multiplying the primes 2 × 2 × 3 × 3 × 19.
How is 684 represented in binary and hexadecimal?
684 converts to 1010101100 in binary and 2AC in hexadecimal, which are helpful for computer science applications.
Is 684 a perfect square, cube, or triangular number?
684 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 684?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.