1801
1801 is a odd prime number that follows 1800 and precedes 1802. As a prime number, 1801 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1801. 1801 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1801 is represented as 11100001001 in binary and 709 in hexadecimal. Historically, it is written as MDCCCI in Roman numerals.
Factor Analysis
2 FactorsProperties
1801 is prime, so its only factors are 1 and 1801.
Divisible by 2
1801 ends in 1, so it is odd.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
1801 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 10 is not a multiple of 9.
Divisible by 10
1801 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Deficient classification and digit analytics place 1801 within several notable number theory sequences:
Timeline
Deep dive
How 1801 breaks down
1801 carries 2 distinct factors and a digit signature of 10 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100001001 supports bitwise reasoning, hexadecimal 709 aligns with computing notation, and the Roman numeral MDCCCI keeps the encyclopedic tradition alive. These attributes make 1801 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1801 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1796–1806) to tune search ranges, and educators feature 1801 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1801 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 1801
Is 1801 a prime number?
1801 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 1801?
1801 is already prime, so the factorization is simply 1801.
How is 1801 represented in binary and hexadecimal?
1801 converts to 11100001001 in binary and 709 in hexadecimal, which are helpful for computer science applications.
Is 1801 a perfect square, cube, or triangular number?
1801 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1801?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.