1880
1880 is a even composite number that follows 1879 and precedes 1881. It is composed of 16 distinct factors: 1, 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, 940, 1880. Its prime factorization can be written as 2^3 × 5 × 47. 1880 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1880 is represented as 11101011000 in binary and 758 in hexadecimal. Historically, it is written as MDCCCLXXX in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 5 × 47) reveals 5 prime building blocks.
Divisible by 2
1880 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
1880 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
1880 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 1880 within several notable number theory sequences:
Timeline
Deep dive
How 1880 breaks down
1880 carries 16 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 2440, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11101011000 supports bitwise reasoning, hexadecimal 758 aligns with computing notation, and the Roman numeral MDCCCLXXX keeps the encyclopedic tradition alive. These attributes make 1880 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1880 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1875–1885) to tune search ranges, and educators feature 1880 in worksheets about factor trees. Its binary footprint of length 11 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 1880 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 1880
Is 1880 a prime number?
1880 is composite with 16 total factors and the prime factorization 2^3 × 5 × 47.
What is the prime factorization of 1880?
It breaks down as 2^3 × 5 × 47, multiplying the primes 2 × 2 × 2 × 5 × 47.
How is 1880 represented in binary and hexadecimal?
1880 converts to 11101011000 in binary and 758 in hexadecimal, which are helpful for computer science applications.
Is 1880 a perfect square, cube, or triangular number?
1880 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1880?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.