1755
1755 is a odd composite number that follows 1754 and precedes 1756. It is composed of 16 distinct factors: 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755. Its prime factorization can be written as 3^3 × 5 × 13. 1755 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1755 is represented as 11011011011 in binary and 6DB in hexadecimal. Historically, it is written as MDCCLV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (3^3 × 5 × 13) reveals 5 prime building blocks.
Divisible by 2
1755 ends in 5, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 55 are not divisible by 4.
Divisible by 5
1755 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 18 is a multiple of 9.
Divisible by 10
1755 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Deficient classification and digit analytics place 1755 within several notable number theory sequences:
Timeline
Deep dive
How 1755 breaks down
1755 carries 16 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 1605, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011011011 supports bitwise reasoning, hexadecimal 6DB aligns with computing notation, and the Roman numeral MDCCLV keeps the encyclopedic tradition alive. These attributes make 1755 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1755 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1750–1760) to tune search ranges, and educators feature 1755 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 1755 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 1755
Is 1755 a prime number?
1755 is composite with 16 total factors and the prime factorization 3^3 × 5 × 13.
What is the prime factorization of 1755?
It breaks down as 3^3 × 5 × 13, multiplying the primes 3 × 3 × 3 × 5 × 13.
How is 1755 represented in binary and hexadecimal?
1755 converts to 11011011011 in binary and 6DB in hexadecimal, which are helpful for computer science applications.
Is 1755 a perfect square, cube, or triangular number?
1755 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1755?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.