27648
27648 is a even composite number that follows 27647 and precedes 27649. It is composed of 44 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, 1024, 1152, 1536, 1728, 2304, 3072, 3456, 4608, 6912, 9216, 13824, 27648. Its prime factorization can be written as 2^10 × 3^3. 27648 is classified as a abundant number based on the sum of its proper divisors. In computer science, 27648 is represented as 110110000000000 in binary and 6C00 in hexadecimal.
Factor Analysis
44 FactorsProperties
The prime factorization (2^10 × 3^3) reveals 13 prime building blocks.
Divisible by 2
27648 ends in 8, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
27648 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 27 is a multiple of 9.
Divisible by 10
27648 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 27648 within several notable number theory sequences:
Timeline
Deep dive
How 27648 breaks down
27648 carries 44 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 54232, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110000000000 supports bitwise reasoning, hexadecimal 6C00 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 27648 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 27648 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (27643–27653) to tune search ranges, and educators feature 27648 in worksheets about factor trees. Its binary footprint of length 15 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 27648 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 27648
Is 27648 a prime number?
27648 is composite with 44 total factors and the prime factorization 2^10 × 3^3.
What is the prime factorization of 27648?
It breaks down as 2^10 × 3^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.
How is 27648 represented in binary and hexadecimal?
27648 converts to 110110000000000 in binary and 6C00 in hexadecimal, which are helpful for computer science applications.
Is 27648 a perfect square, cube, or triangular number?
27648 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 27648?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.