1890
1890 is a even composite number that follows 1889 and precedes 1891. It is composed of 32 distinct factors: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890. Its prime factorization can be written as 2 × 3^3 × 5 × 7. 1890 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1890 is represented as 11101100010 in binary and 762 in hexadecimal. Historically, it is written as MDCCCXC in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2 × 3^3 × 5 × 7) reveals 6 prime building blocks.
Divisible by 2
1890 ends in 0, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 90 are not divisible by 4.
Divisible by 5
1890 ends in 0, so it is divisible by 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 18 is a multiple of 9.
Divisible by 10
1890 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 1890 within several notable number theory sequences:
Timeline
Deep dive
How 1890 breaks down
1890 carries 32 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 3870, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11101100010 supports bitwise reasoning, hexadecimal 762 aligns with computing notation, and the Roman numeral MDCCCXC keeps the encyclopedic tradition alive. These attributes make 1890 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1890 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1885–1895) to tune search ranges, and educators feature 1890 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 1890 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 1890
Is 1890 a prime number?
1890 is composite with 32 total factors and the prime factorization 2 × 3^3 × 5 × 7.
What is the prime factorization of 1890?
It breaks down as 2 × 3^3 × 5 × 7, multiplying the primes 2 × 3 × 3 × 3 × 5 × 7.
How is 1890 represented in binary and hexadecimal?
1890 converts to 11101100010 in binary and 762 in hexadecimal, which are helpful for computer science applications.
Is 1890 a perfect square, cube, or triangular number?
1890 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1890?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.