1746
1746 is a even composite number that follows 1745 and precedes 1747. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746. Its prime factorization can be written as 2 × 3^2 × 97. 1746 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1746 is represented as 11011010010 in binary and 6D2 in hexadecimal. Historically, it is written as MDCCXLVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 97) reveals 4 prime building blocks.
Divisible by 2
1746 ends in 6, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 46 are not divisible by 4.
Divisible by 5
1746 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
1746 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Abundant classification and digit analytics place 1746 within several notable number theory sequences:
Timeline
Deep dive
How 1746 breaks down
1746 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2076, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011010010 supports bitwise reasoning, hexadecimal 6D2 aligns with computing notation, and the Roman numeral MDCCXLVI keeps the encyclopedic tradition alive. These attributes make 1746 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1746 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1741–1751) to tune search ranges, and educators feature 1746 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, Abundant numbers) help historians, numerologists, and trivia writers tie 1746 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 1746
Is 1746 a prime number?
1746 is composite with 12 total factors and the prime factorization 2 × 3^2 × 97.
What is the prime factorization of 1746?
It breaks down as 2 × 3^2 × 97, multiplying the primes 2 × 3 × 3 × 97.
How is 1746 represented in binary and hexadecimal?
1746 converts to 11011010010 in binary and 6D2 in hexadecimal, which are helpful for computer science applications.
Is 1746 a perfect square, cube, or triangular number?
1746 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1746?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.