1684
1684 is a even composite number that follows 1683 and precedes 1685. It is composed of 6 distinct factors: 1, 2, 4, 421, 842, 1684. Its prime factorization can be written as 2^2 × 421. 1684 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1684 is represented as 11010010100 in binary and 694 in hexadecimal. Historically, it is written as MDCLXXXIV in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 421) reveals 3 prime building blocks.
Divisible by 2
1684 ends in 4, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
1684 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 19 is not a multiple of 9.
Divisible by 10
1684 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 1684 within several notable number theory sequences:
Timeline
Deep dive
How 1684 breaks down
1684 carries 6 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 1270, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010010100 supports bitwise reasoning, hexadecimal 694 aligns with computing notation, and the Roman numeral MDCLXXXIV keeps the encyclopedic tradition alive. These attributes make 1684 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1684 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1679–1689) to tune search ranges, and educators feature 1684 in worksheets about factor trees. Its binary footprint of length 11 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 1684 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 1684
Is 1684 a prime number?
1684 is composite with 6 total factors and the prime factorization 2^2 × 421.
What is the prime factorization of 1684?
It breaks down as 2^2 × 421, multiplying the primes 2 × 2 × 421.
How is 1684 represented in binary and hexadecimal?
1684 converts to 11010010100 in binary and 694 in hexadecimal, which are helpful for computer science applications.
Is 1684 a perfect square, cube, or triangular number?
1684 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1684?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.