7684
7684 is a even composite number that follows 7683 and precedes 7685. It is composed of 12 distinct factors: 1, 2, 4, 17, 34, 68, 113, 226, 452, 1921, 3842, 7684. Its prime factorization can be written as 2^2 × 17 × 113. 7684 is classified as a deficient number based on the sum of its proper divisors. In computer science, 7684 is represented as 1111000000100 in binary and 1E04 in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 17 × 113) reveals 4 prime building blocks.
Divisible by 2
7684 ends in 4, so it is even.
Divisible by 3
The digit sum 25 is not a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
7684 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 25 is not a multiple of 9.
Divisible by 10
7684 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 7684 within several notable number theory sequences:
Timeline
Deep dive
How 7684 breaks down
7684 carries 12 distinct factors and a digit signature of 25 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 6680, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111000000100 supports bitwise reasoning, hexadecimal 1E04 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7684 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7684 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7679–7689) to tune search ranges, and educators feature 7684 in worksheets about factor trees. Its binary footprint of length 13 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 7684 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 7684
Is 7684 a prime number?
7684 is composite with 12 total factors and the prime factorization 2^2 × 17 × 113.
What is the prime factorization of 7684?
It breaks down as 2^2 × 17 × 113, multiplying the primes 2 × 2 × 17 × 113.
How is 7684 represented in binary and hexadecimal?
7684 converts to 1111000000100 in binary and 1E04 in hexadecimal, which are helpful for computer science applications.
Is 7684 a perfect square, cube, or triangular number?
7684 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7684?
The digits sum to 25, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.