3880
3880 is a even composite number that follows 3879 and precedes 3881. It is composed of 16 distinct factors: 1, 2, 4, 5, 8, 10, 20, 40, 97, 194, 388, 485, 776, 970, 1940, 3880. Its prime factorization can be written as 2^3 × 5 × 97. 3880 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3880 is represented as 111100101000 in binary and F28 in hexadecimal. Historically, it is written as MMMDCCCLXXX in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 5 × 97) reveals 5 prime building blocks.
Divisible by 2
3880 ends in 0, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
3880 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 19 is not a multiple of 9.
Divisible by 10
3880 ends in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 3880 within several notable number theory sequences:
Timeline
Deep dive
How 3880 breaks down
3880 carries 16 distinct factors and a digit signature of 19 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 4940, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111100101000 supports bitwise reasoning, hexadecimal F28 aligns with computing notation, and the Roman numeral MMMDCCCLXXX keeps the encyclopedic tradition alive. These attributes make 3880 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3880 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3875–3885) to tune search ranges, and educators feature 3880 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 3880 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 3880
Is 3880 a prime number?
3880 is composite with 16 total factors and the prime factorization 2^3 × 5 × 97.
What is the prime factorization of 3880?
It breaks down as 2^3 × 5 × 97, multiplying the primes 2 × 2 × 2 × 5 × 97.
How is 3880 represented in binary and hexadecimal?
3880 converts to 111100101000 in binary and F28 in hexadecimal, which are helpful for computer science applications.
Is 3880 a perfect square, cube, or triangular number?
3880 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3880?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.