3504
3504 is a even composite number that follows 3503 and precedes 3505. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 73, 146, 219, 292, 438, 584, 876, 1168, 1752, 3504. Its prime factorization can be written as 2^4 × 3 × 73. 3504 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3504 is represented as 110110110000 in binary and DB0 in hexadecimal. Historically, it is written as MMMDIV in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 73) reveals 6 prime building blocks.
Divisible by 2
3504 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
3504 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
3504 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Abundant classification and digit analytics place 3504 within several notable number theory sequences:
Timeline
Deep dive
How 3504 breaks down
3504 carries 20 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 5672, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110110000 supports bitwise reasoning, hexadecimal DB0 aligns with computing notation, and the Roman numeral MMMDIV keeps the encyclopedic tradition alive. These attributes make 3504 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3504 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3499–3509) to tune search ranges, and educators feature 3504 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 3504 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 3504
Is 3504 a prime number?
3504 is composite with 20 total factors and the prime factorization 2^4 × 3 × 73.
What is the prime factorization of 3504?
It breaks down as 2^4 × 3 × 73, multiplying the primes 2 × 2 × 2 × 2 × 3 × 73.
How is 3504 represented in binary and hexadecimal?
3504 converts to 110110110000 in binary and DB0 in hexadecimal, which are helpful for computer science applications.
Is 3504 a perfect square, cube, or triangular number?
3504 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3504?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.