984
984 is a even composite number that follows 983 and precedes 985. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984. Its prime factorization can be written as 2^3 × 3 × 41. 984 is classified as a abundant number based on the sum of its proper divisors. In computer science, 984 is represented as 1111011000 in binary and 3D8 in hexadecimal. Historically, it is written as CMLXXXIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 41) reveals 5 prime building blocks.
Divisible by 2
984 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
984 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
984 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 984 within several notable number theory sequences:
Timeline
Deep dive
How 984 breaks down
984 carries 16 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1536, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111011000 supports bitwise reasoning, hexadecimal 3D8 aligns with computing notation, and the Roman numeral CMLXXXIV keeps the encyclopedic tradition alive. These attributes make 984 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 984 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (979–989) to tune search ranges, and educators feature 984 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 984 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 984
Is 984 a prime number?
984 is composite with 16 total factors and the prime factorization 2^3 × 3 × 41.
What is the prime factorization of 984?
It breaks down as 2^3 × 3 × 41, multiplying the primes 2 × 2 × 2 × 3 × 41.
How is 984 represented in binary and hexadecimal?
984 converts to 1111011000 in binary and 3D8 in hexadecimal, which are helpful for computer science applications.
Is 984 a perfect square, cube, or triangular number?
984 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 984?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.