3520
3520 is a even composite number that follows 3519 and precedes 3521. It is composed of 28 distinct factors: 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 160, 176, 220, 320, 352, 440, 704, 880, 1760, 3520. Its prime factorization can be written as 2^6 × 5 × 11. 3520 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3520 is represented as 110111000000 in binary and DC0 in hexadecimal. Historically, it is written as MMMDXX in Roman numerals.
Factor Analysis
28 FactorsProperties
The prime factorization (2^6 × 5 × 11) reveals 8 prime building blocks.
Divisible by 2
3520 ends in 0, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
3520 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 10 is not a multiple of 9.
Divisible by 10
3520 ends in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 3520 within several notable number theory sequences:
Timeline
Deep dive
How 3520 breaks down
3520 carries 28 distinct factors and a digit signature of 10 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 5624, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110111000000 supports bitwise reasoning, hexadecimal DC0 aligns with computing notation, and the Roman numeral MMMDXX keeps the encyclopedic tradition alive. These attributes make 3520 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3520 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3515–3525) to tune search ranges, and educators feature 3520 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 3520 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 3520
Is 3520 a prime number?
3520 is composite with 28 total factors and the prime factorization 2^6 × 5 × 11.
What is the prime factorization of 3520?
It breaks down as 2^6 × 5 × 11, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 5 × 11.
How is 3520 represented in binary and hexadecimal?
3520 converts to 110111000000 in binary and DC0 in hexadecimal, which are helpful for computer science applications.
Is 3520 a perfect square, cube, or triangular number?
3520 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3520?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.