384
384 is a even composite number that follows 383 and precedes 385. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. Its prime factorization can be written as 2^7 × 3. 384 is classified as a abundant number based on the sum of its proper divisors. In computer science, 384 is represented as 110000000 in binary and 180 in hexadecimal. Historically, it is written as CCCLXXXIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^7 × 3) reveals 8 prime building blocks.
Divisible by 2
384 ends in 4, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 84 form a multiple of 4.
Divisible by 5
384 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 15 is not a multiple of 9.
Divisible by 10
384 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 384 within several notable number theory sequences:
Timeline
Deep dive
How 384 breaks down
384 carries 16 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 636, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110000000 supports bitwise reasoning, hexadecimal 180 aligns with computing notation, and the Roman numeral CCCLXXXIV keeps the encyclopedic tradition alive. These attributes make 384 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 384 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (379–389) to tune search ranges, and educators feature 384 in worksheets about factor trees. Its binary footprint of length 9 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 384 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 384
Is 384 a prime number?
384 is composite with 16 total factors and the prime factorization 2^7 × 3.
What is the prime factorization of 384?
It breaks down as 2^7 × 3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.
How is 384 represented in binary and hexadecimal?
384 converts to 110000000 in binary and 180 in hexadecimal, which are helpful for computer science applications.
Is 384 a perfect square, cube, or triangular number?
384 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 384?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.