1745
1745 is a odd composite number that follows 1744 and precedes 1746. It is composed of 4 distinct factors: 1, 5, 349, 1745. Its prime factorization can be written as 5 × 349. 1745 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1745 is represented as 11011010001 in binary and 6D1 in hexadecimal. Historically, it is written as MDCCXLV in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (5 × 349) reveals 2 prime building blocks.
Divisible by 2
1745 ends in 5, so it is odd.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 45 are not divisible by 4.
Divisible by 5
1745 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 17 is not a multiple of 9.
Divisible by 10
1745 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Deficient classification and digit analytics place 1745 within several notable number theory sequences:
Timeline
Deep dive
How 1745 breaks down
1745 carries 4 distinct factors and a digit signature of 17 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 355, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011010001 supports bitwise reasoning, hexadecimal 6D1 aligns with computing notation, and the Roman numeral MDCCXLV keeps the encyclopedic tradition alive. These attributes make 1745 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1745 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1740–1750) to tune search ranges, and educators feature 1745 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 1745 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 1745
Is 1745 a prime number?
1745 is composite with 4 total factors and the prime factorization 5 × 349.
What is the prime factorization of 1745?
It breaks down as 5 × 349, multiplying the primes 5 × 349.
How is 1745 represented in binary and hexadecimal?
1745 converts to 11011010001 in binary and 6D1 in hexadecimal, which are helpful for computer science applications.
Is 1745 a perfect square, cube, or triangular number?
1745 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1745?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.