3288
3288 is a even composite number that follows 3287 and precedes 3289. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 137, 274, 411, 548, 822, 1096, 1644, 3288. Its prime factorization can be written as 2^3 × 3 × 137. 3288 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3288 is represented as 110011011000 in binary and CD8 in hexadecimal. Historically, it is written as MMMCCLXXXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 137) reveals 5 prime building blocks.
Divisible by 2
3288 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
3288 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 21 is not a multiple of 9.
Divisible by 10
3288 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 3288 within several notable number theory sequences:
Timeline
Deep dive
How 3288 breaks down
3288 carries 16 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 4992, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110011011000 supports bitwise reasoning, hexadecimal CD8 aligns with computing notation, and the Roman numeral MMMCCLXXXVIII keeps the encyclopedic tradition alive. These attributes make 3288 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3288 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3283–3293) to tune search ranges, and educators feature 3288 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 3288 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 3288
Is 3288 a prime number?
3288 is composite with 16 total factors and the prime factorization 2^3 × 3 × 137.
What is the prime factorization of 3288?
It breaks down as 2^3 × 3 × 137, multiplying the primes 2 × 2 × 2 × 3 × 137.
How is 3288 represented in binary and hexadecimal?
3288 converts to 110011011000 in binary and CD8 in hexadecimal, which are helpful for computer science applications.
Is 3288 a perfect square, cube, or triangular number?
3288 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3288?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.