3312
3312 is a even composite number that follows 3311 and precedes 3313. It is composed of 30 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69, 72, 92, 138, 144, 184, 207, 276, 368, 414, 552, 828, 1104, 1656, 3312. Its prime factorization can be written as 2^4 × 3^2 × 23. 3312 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3312 is represented as 110011110000 in binary and CF0 in hexadecimal. Historically, it is written as MMMCCCXII in Roman numerals.
Factor Analysis
30 FactorsProperties
The prime factorization (2^4 × 3^2 × 23) reveals 7 prime building blocks.
Divisible by 2
3312 ends in 2, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 12 form a multiple of 4.
Divisible by 5
3312 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
3312 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 3312 within several notable number theory sequences:
Timeline
Deep dive
How 3312 breaks down
3312 carries 30 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 6360, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110011110000 supports bitwise reasoning, hexadecimal CF0 aligns with computing notation, and the Roman numeral MMMCCCXII keeps the encyclopedic tradition alive. These attributes make 3312 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3312 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3307–3317) to tune search ranges, and educators feature 3312 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 3312 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 3312
Is 3312 a prime number?
3312 is composite with 30 total factors and the prime factorization 2^4 × 3^2 × 23.
What is the prime factorization of 3312?
It breaks down as 2^4 × 3^2 × 23, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 23.
How is 3312 represented in binary and hexadecimal?
3312 converts to 110011110000 in binary and CF0 in hexadecimal, which are helpful for computer science applications.
Is 3312 a perfect square, cube, or triangular number?
3312 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3312?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.