1815
1815 is a odd composite number that follows 1814 and precedes 1816. It is composed of 12 distinct factors: 1, 3, 5, 11, 15, 33, 55, 121, 165, 363, 605, 1815. Its prime factorization can be written as 3 × 5 × 11^2. 1815 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1815 is represented as 11100010111 in binary and 717 in hexadecimal. Historically, it is written as MDCCCXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3 × 5 × 11^2) reveals 4 prime building blocks.
Divisible by 2
1815 ends in 5, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 15 are not divisible by 4.
Divisible by 5
1815 ends in 5, 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 15 is not a multiple of 9.
Divisible by 10
1815 does not end in 0.
Divisible by 11
The alternating digit sum -11 is a multiple of 11.
Deficient classification and digit analytics place 1815 within several notable number theory sequences:
Timeline
Deep dive
How 1815 breaks down
1815 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 1377, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100010111 supports bitwise reasoning, hexadecimal 717 aligns with computing notation, and the Roman numeral MDCCCXV keeps the encyclopedic tradition alive. These attributes make 1815 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1815 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1810–1820) to tune search ranges, and educators feature 1815 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 1815 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 1815
Is 1815 a prime number?
1815 is composite with 12 total factors and the prime factorization 3 × 5 × 11^2.
What is the prime factorization of 1815?
It breaks down as 3 × 5 × 11^2, multiplying the primes 3 × 5 × 11 × 11.
How is 1815 represented in binary and hexadecimal?
1815 converts to 11100010111 in binary and 717 in hexadecimal, which are helpful for computer science applications.
Is 1815 a perfect square, cube, or triangular number?
1815 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1815?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.