13824
13824 is a even composite number that follows 13823 and precedes 13825. It is composed of 40 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824. Its prime factorization can be written as 2^9 × 3^3. 13824 is classified as a abundant number based on the sum of its proper divisors. In computer science, 13824 is represented as 11011000000000 in binary and 3600 in hexadecimal. It also belongs to the perfect cube sequence.
Factor Analysis
40 FactorsProperties
The prime factorization (2^9 × 3^3) reveals 12 prime building blocks.
Divisible by 2
13824 ends in 4, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
13824 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 18 is a multiple of 9.
Divisible by 10
13824 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 13824 within several notable number theory sequences:
Timeline
Deep dive
How 13824 breaks down
13824 carries 40 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 27096, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011000000000 supports bitwise reasoning, hexadecimal 3600 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 13824 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 13824 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (13819–13829) to tune search ranges, and educators feature 13824 in worksheets about factor trees. Its binary footprint of length 14 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers, Perfect cubes) help historians, numerologists, and trivia writers tie 13824 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 13824
Is 13824 a prime number?
13824 is composite with 40 total factors and the prime factorization 2^9 × 3^3.
What is the prime factorization of 13824?
It breaks down as 2^9 × 3^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.
How is 13824 represented in binary and hexadecimal?
13824 converts to 11011000000000 in binary and 3600 in hexadecimal, which are helpful for computer science applications.
Is 13824 a perfect square, cube, or triangular number?
13824 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 13824?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.