9216
9216 is a even composite number that follows 9215 and precedes 9217. It is composed of 33 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2304, 3072, 4608, 9216. Its prime factorization can be written as 2^10 × 3^2. 9216 is classified as a abundant number based on the sum of its proper divisors. In computer science, 9216 is represented as 10010000000000 in binary and 2400 in hexadecimal. It also belongs to the perfect square sequence.
Factor Analysis
33 FactorsProperties
The prime factorization (2^10 × 3^2) reveals 12 prime building blocks.
Divisible by 2
9216 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
9216 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
9216 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 9216 within several notable number theory sequences:
Timeline
Deep dive
How 9216 breaks down
9216 carries 33 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 17395, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010000000000 supports bitwise reasoning, hexadecimal 2400 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 9216 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 9216 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (9211–9221) to tune search ranges, and educators feature 9216 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 squares) help historians, numerologists, and trivia writers tie 9216 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 9216
Is 9216 a prime number?
9216 is composite with 33 total factors and the prime factorization 2^10 × 3^2.
What is the prime factorization of 9216?
It breaks down as 2^10 × 3^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3.
How is 9216 represented in binary and hexadecimal?
9216 converts to 10010000000000 in binary and 2400 in hexadecimal, which are helpful for computer science applications.
Is 9216 a perfect square, cube, or triangular number?
9216 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 9216?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.