3680
3680 is a even composite number that follows 3679 and precedes 3681. It is composed of 24 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, 3680. Its prime factorization can be written as 2^5 × 5 × 23. 3680 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3680 is represented as 111001100000 in binary and E60 in hexadecimal. Historically, it is written as MMMDCLXXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 5 × 23) reveals 7 prime building blocks.
Divisible by 2
3680 ends in 0, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
3680 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 17 is not a multiple of 9.
Divisible by 10
3680 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 3680 within several notable number theory sequences:
Timeline
Deep dive
How 3680 breaks down
3680 carries 24 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 5392, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001100000 supports bitwise reasoning, hexadecimal E60 aligns with computing notation, and the Roman numeral MMMDCLXXX keeps the encyclopedic tradition alive. These attributes make 3680 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3680 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3675–3685) to tune search ranges, and educators feature 3680 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 3680 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 3680
Is 3680 a prime number?
3680 is composite with 24 total factors and the prime factorization 2^5 × 5 × 23.
What is the prime factorization of 3680?
It breaks down as 2^5 × 5 × 23, multiplying the primes 2 × 2 × 2 × 2 × 2 × 5 × 23.
How is 3680 represented in binary and hexadecimal?
3680 converts to 111001100000 in binary and E60 in hexadecimal, which are helpful for computer science applications.
Is 3680 a perfect square, cube, or triangular number?
3680 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3680?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.