3904
3904 is a even composite number that follows 3903 and precedes 3905. It is composed of 14 distinct factors: 1, 2, 4, 8, 16, 32, 61, 64, 122, 244, 488, 976, 1952, 3904. Its prime factorization can be written as 2^6 × 61. 3904 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3904 is represented as 111101000000 in binary and F40 in hexadecimal. Historically, it is written as MMMCMIV in Roman numerals.
Factor Analysis
14 FactorsProperties
The prime factorization (2^6 × 61) reveals 7 prime building blocks.
Divisible by 2
3904 ends in 4, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
3904 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 16 is not a multiple of 9.
Divisible by 10
3904 does not end in 0.
Divisible by 11
The alternating digit sum -10 is not a multiple of 11.
Abundant classification and digit analytics place 3904 within several notable number theory sequences:
Timeline
Deep dive
How 3904 breaks down
3904 carries 14 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 3970, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111101000000 supports bitwise reasoning, hexadecimal F40 aligns with computing notation, and the Roman numeral MMMCMIV keeps the encyclopedic tradition alive. These attributes make 3904 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3904 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3899–3909) to tune search ranges, and educators feature 3904 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 3904 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 3904
Is 3904 a prime number?
3904 is composite with 14 total factors and the prime factorization 2^6 × 61.
What is the prime factorization of 3904?
It breaks down as 2^6 × 61, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 61.
How is 3904 represented in binary and hexadecimal?
3904 converts to 111101000000 in binary and F40 in hexadecimal, which are helpful for computer science applications.
Is 3904 a perfect square, cube, or triangular number?
3904 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3904?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.