3984
3984 is a even composite number that follows 3983 and precedes 3985. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 83, 166, 249, 332, 498, 664, 996, 1328, 1992, 3984. Its prime factorization can be written as 2^4 × 3 × 83. 3984 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3984 is represented as 111110010000 in binary and F90 in hexadecimal. Historically, it is written as MMMCMLXXXIV in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 83) reveals 6 prime building blocks.
Divisible by 2
3984 ends in 4, so it is even.
Divisible by 3
The digit sum 24 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
3984 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 24 is not a multiple of 9.
Divisible by 10
3984 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 3984 within several notable number theory sequences:
Timeline
Deep dive
How 3984 breaks down
3984 carries 20 distinct factors and a digit signature of 24 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 6432, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110010000 supports bitwise reasoning, hexadecimal F90 aligns with computing notation, and the Roman numeral MMMCMLXXXIV keeps the encyclopedic tradition alive. These attributes make 3984 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3984 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3979–3989) to tune search ranges, and educators feature 3984 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 3984 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 3984
Is 3984 a prime number?
3984 is composite with 20 total factors and the prime factorization 2^4 × 3 × 83.
What is the prime factorization of 3984?
It breaks down as 2^4 × 3 × 83, multiplying the primes 2 × 2 × 2 × 2 × 3 × 83.
How is 3984 represented in binary and hexadecimal?
3984 converts to 111110010000 in binary and F90 in hexadecimal, which are helpful for computer science applications.
Is 3984 a perfect square, cube, or triangular number?
3984 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3984?
The digits sum to 24, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.