3072
3072 is a even composite number that follows 3071 and precedes 3073. It is composed of 22 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 3072. Its prime factorization can be written as 2^10 × 3. 3072 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3072 is represented as 110000000000 in binary and C00 in hexadecimal. Historically, it is written as MMMLXXII in Roman numerals.
Factor Analysis
22 FactorsProperties
The prime factorization (2^10 × 3) reveals 11 prime building blocks.
Divisible by 2
3072 ends in 2, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
3072 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
3072 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 3072 within several notable number theory sequences:
Timeline
Deep dive
How 3072 breaks down
3072 carries 22 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 5116, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110000000000 supports bitwise reasoning, hexadecimal C00 aligns with computing notation, and the Roman numeral MMMLXXII keeps the encyclopedic tradition alive. These attributes make 3072 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3072 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3067–3077) to tune search ranges, and educators feature 3072 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 3072 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 3072
Is 3072 a prime number?
3072 is composite with 22 total factors and the prime factorization 2^10 × 3.
What is the prime factorization of 3072?
It breaks down as 2^10 × 3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.
How is 3072 represented in binary and hexadecimal?
3072 converts to 110000000000 in binary and C00 in hexadecimal, which are helpful for computer science applications.
Is 3072 a perfect square, cube, or triangular number?
3072 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3072?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.