3078
3078 is a even composite number that follows 3077 and precedes 3079. It is composed of 20 distinct factors: 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078. Its prime factorization can be written as 2 × 3^4 × 19. 3078 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3078 is represented as 110000000110 in binary and C06 in hexadecimal. Historically, it is written as MMMLXXVIII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2 × 3^4 × 19) reveals 6 prime building blocks.
Divisible by 2
3078 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
3078 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 18 is a multiple of 9.
Divisible by 10
3078 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 3078 within several notable number theory sequences:
Timeline
Deep dive
How 3078 breaks down
3078 carries 20 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4182, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110000000110 supports bitwise reasoning, hexadecimal C06 aligns with computing notation, and the Roman numeral MMMLXXVIII keeps the encyclopedic tradition alive. These attributes make 3078 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3078 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3073–3083) to tune search ranges, and educators feature 3078 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 3078 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 3078
Is 3078 a prime number?
3078 is composite with 20 total factors and the prime factorization 2 × 3^4 × 19.
What is the prime factorization of 3078?
It breaks down as 2 × 3^4 × 19, multiplying the primes 2 × 3 × 3 × 3 × 3 × 19.
How is 3078 represented in binary and hexadecimal?
3078 converts to 110000000110 in binary and C06 in hexadecimal, which are helpful for computer science applications.
Is 3078 a perfect square, cube, or triangular number?
3078 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3078?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.