3216
3216 is a even composite number that follows 3215 and precedes 3217. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 67, 134, 201, 268, 402, 536, 804, 1072, 1608, 3216. Its prime factorization can be written as 2^4 × 3 × 67. 3216 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3216 is represented as 110010010000 in binary and C90 in hexadecimal. Historically, it is written as MMMCCXVI in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 67) reveals 6 prime building blocks.
Divisible by 2
3216 ends in 6, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
3216 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 12 is not a multiple of 9.
Divisible by 10
3216 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 3216 within several notable number theory sequences:
Timeline
Deep dive
How 3216 breaks down
3216 carries 20 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 5216, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010010000 supports bitwise reasoning, hexadecimal C90 aligns with computing notation, and the Roman numeral MMMCCXVI keeps the encyclopedic tradition alive. These attributes make 3216 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3216 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3211–3221) to tune search ranges, and educators feature 3216 in worksheets about factor trees. Its binary footprint of length 12 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 3216 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 3216
Is 3216 a prime number?
3216 is composite with 20 total factors and the prime factorization 2^4 × 3 × 67.
What is the prime factorization of 3216?
It breaks down as 2^4 × 3 × 67, multiplying the primes 2 × 2 × 2 × 2 × 3 × 67.
How is 3216 represented in binary and hexadecimal?
3216 converts to 110010010000 in binary and C90 in hexadecimal, which are helpful for computer science applications.
Is 3216 a perfect square, cube, or triangular number?
3216 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3216?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.