1984
1984 is a even composite number that follows 1983 and precedes 1985. It is composed of 14 distinct factors: 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984. Its prime factorization can be written as 2^6 × 31. 1984 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1984 is represented as 11111000000 in binary and 7C0 in hexadecimal. Historically, it is written as MCMLXXXIV in Roman numerals.
Factor Analysis
14 FactorsProperties
The prime factorization (2^6 × 31) reveals 7 prime building blocks.
Divisible by 2
1984 ends in 4, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
1984 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 22 is not a multiple of 9.
Divisible by 10
1984 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 1984 within several notable number theory sequences:
Timeline
Deep dive
How 1984 breaks down
1984 carries 14 distinct factors and a digit signature of 22 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 2080, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11111000000 supports bitwise reasoning, hexadecimal 7C0 aligns with computing notation, and the Roman numeral MCMLXXXIV keeps the encyclopedic tradition alive. These attributes make 1984 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1984 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1979–1989) to tune search ranges, and educators feature 1984 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, Abundant numbers) help historians, numerologists, and trivia writers tie 1984 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 1984
Is 1984 a prime number?
1984 is composite with 14 total factors and the prime factorization 2^6 × 31.
What is the prime factorization of 1984?
It breaks down as 2^6 × 31, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 31.
How is 1984 represented in binary and hexadecimal?
1984 converts to 11111000000 in binary and 7C0 in hexadecimal, which are helpful for computer science applications.
Is 1984 a perfect square, cube, or triangular number?
1984 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1984?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.