216
216 is a even composite number that follows 215 and precedes 217. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. Its prime factorization can be written as 2^3 × 3^3. 216 is classified as a abundant number based on the sum of its proper divisors. In computer science, 216 is represented as 11011000 in binary and D8 in hexadecimal. Historically, it is written as CCXVI in Roman numerals. It also belongs to the perfect cube sequence.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3^3) reveals 6 prime building blocks.
Divisible by 2
216 ends in 6, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
216 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 9 is a multiple of 9.
Divisible by 10
216 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 216 within several notable number theory sequences:
Timeline
Deep dive
How 216 breaks down
216 carries 16 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 384, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011000 supports bitwise reasoning, hexadecimal D8 aligns with computing notation, and the Roman numeral CCXVI keeps the encyclopedic tradition alive. These attributes make 216 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 216 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (211–221) to tune search ranges, and educators feature 216 in worksheets about factor trees. Its binary footprint of length 8 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 216 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 216
Is 216 a prime number?
216 is composite with 16 total factors and the prime factorization 2^3 × 3^3.
What is the prime factorization of 216?
It breaks down as 2^3 × 3^3, multiplying the primes 2 × 2 × 2 × 3 × 3 × 3.
How is 216 represented in binary and hexadecimal?
216 converts to 11011000 in binary and D8 in hexadecimal, which are helpful for computer science applications.
Is 216 a perfect square, cube, or triangular number?
216 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 216?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.