84
84 is a even composite number that follows 83 and precedes 85. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Its prime factorization can be written as 2^2 × 3 × 7. 84 is classified as a abundant number based on the sum of its proper divisors. In computer science, 84 is represented as 1010100 in binary and 54 in hexadecimal. Historically, it is written as LXXXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 7) reveals 4 prime building blocks.
Divisible by 2
84 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
84 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 12 is not a multiple of 9.
Divisible by 10
84 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 84 within several notable number theory sequences:
Timeline
Deep dive
How 84 breaks down
84 carries 12 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 140, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010100 supports bitwise reasoning, hexadecimal 54 aligns with computing notation, and the Roman numeral LXXXIV keeps the encyclopedic tradition alive. These attributes make 84 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 84 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (79–89) to tune search ranges, and educators feature 84 in worksheets about factor trees. Its binary footprint of length 7 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 84 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 84
Is 84 a prime number?
84 is composite with 12 total factors and the prime factorization 2^2 × 3 × 7.
What is the prime factorization of 84?
It breaks down as 2^2 × 3 × 7, multiplying the primes 2 × 2 × 3 × 7.
How is 84 represented in binary and hexadecimal?
84 converts to 1010100 in binary and 54 in hexadecimal, which are helpful for computer science applications.
Is 84 a perfect square, cube, or triangular number?
84 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 84?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.