1800
1800 is a even composite number that follows 1799 and precedes 1801. It is composed of 36 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800. Its prime factorization can be written as 2^3 × 3^2 × 5^2. 1800 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1800 is represented as 11100001000 in binary and 708 in hexadecimal. Historically, it is written as MDCCC in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^3 × 3^2 × 5^2) reveals 7 prime building blocks.
Divisible by 2
1800 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
1800 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 9 is a multiple of 9.
Divisible by 10
1800 ends in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 1800 within several notable number theory sequences:
Timeline
Deep dive
How 1800 breaks down
1800 carries 36 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4245, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100001000 supports bitwise reasoning, hexadecimal 708 aligns with computing notation, and the Roman numeral MDCCC keeps the encyclopedic tradition alive. These attributes make 1800 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1800 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1795–1805) to tune search ranges, and educators feature 1800 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 1800 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 1800
Is 1800 a prime number?
1800 is composite with 36 total factors and the prime factorization 2^3 × 3^2 × 5^2.
What is the prime factorization of 1800?
It breaks down as 2^3 × 3^2 × 5^2, multiplying the primes 2 × 2 × 2 × 3 × 3 × 5 × 5.
How is 1800 represented in binary and hexadecimal?
1800 converts to 11100001000 in binary and 708 in hexadecimal, which are helpful for computer science applications.
Is 1800 a perfect square, cube, or triangular number?
1800 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1800?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.