1808
1808 is a even composite number that follows 1807 and precedes 1809. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 113, 226, 452, 904, 1808. Its prime factorization can be written as 2^4 × 113. 1808 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1808 is represented as 11100010000 in binary and 710 in hexadecimal. Historically, it is written as MDCCCVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 113) reveals 5 prime building blocks.
Divisible by 2
1808 ends in 8, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
1808 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 17 is not a multiple of 9.
Divisible by 10
1808 does not end in 0.
Divisible by 11
The alternating digit sum -15 is not a multiple of 11.
Deficient classification and digit analytics place 1808 within several notable number theory sequences:
Timeline
Deep dive
How 1808 breaks down
1808 carries 10 distinct factors and a digit signature of 17 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 1726, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100010000 supports bitwise reasoning, hexadecimal 710 aligns with computing notation, and the Roman numeral MDCCCVIII keeps the encyclopedic tradition alive. These attributes make 1808 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1808 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1803–1813) to tune search ranges, and educators feature 1808 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, Deficient numbers) help historians, numerologists, and trivia writers tie 1808 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 1808
Is 1808 a prime number?
1808 is composite with 10 total factors and the prime factorization 2^4 × 113.
What is the prime factorization of 1808?
It breaks down as 2^4 × 113, multiplying the primes 2 × 2 × 2 × 2 × 113.
How is 1808 represented in binary and hexadecimal?
1808 converts to 11100010000 in binary and 710 in hexadecimal, which are helpful for computer science applications.
Is 1808 a perfect square, cube, or triangular number?
1808 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1808?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.