27216
27216 is a even composite number that follows 27215 and precedes 27217. It is composed of 60 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 243, 252, 324, 336, 378, 432, 486, 504, 567, 648, 756, 972, 1008, 1134, 1296, 1512, 1701, 1944, 2268, 3024, 3402, 3888, 4536, 6804, 9072, 13608, 27216. Its prime factorization can be written as 2^4 × 3^5 × 7. 27216 is classified as a abundant number based on the sum of its proper divisors. In computer science, 27216 is represented as 110101001010000 in binary and 6A50 in hexadecimal.
Factor Analysis
60 FactorsProperties
The prime factorization (2^4 × 3^5 × 7) reveals 10 prime building blocks.
Divisible by 2
27216 ends in 6, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
27216 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
27216 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 27216 within several notable number theory sequences:
Timeline
Deep dive
How 27216 breaks down
27216 carries 60 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 63056, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101001010000 supports bitwise reasoning, hexadecimal 6A50 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 27216 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 27216 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (27211–27221) to tune search ranges, and educators feature 27216 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 27216 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 27216
Is 27216 a prime number?
27216 is composite with 60 total factors and the prime factorization 2^4 × 3^5 × 7.
What is the prime factorization of 27216?
It breaks down as 2^4 × 3^5 × 7, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 7.
How is 27216 represented in binary and hexadecimal?
27216 converts to 110101001010000 in binary and 6A50 in hexadecimal, which are helpful for computer science applications.
Is 27216 a perfect square, cube, or triangular number?
27216 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 27216?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.