1643
1643 is a odd composite number that follows 1642 and precedes 1644. It is composed of 4 distinct factors: 1, 31, 53, 1643. Its prime factorization can be written as 31 × 53. 1643 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1643 is represented as 11001101011 in binary and 66B in hexadecimal. Historically, it is written as MDCXLIII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (31 × 53) reveals 2 prime building blocks.
Divisible by 2
1643 ends in 3, so it is odd.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 43 are not divisible by 4.
Divisible by 5
1643 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 14 is not a multiple of 9.
Divisible by 10
1643 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 1643 within several notable number theory sequences:
Timeline
Deep dive
How 1643 breaks down
1643 carries 4 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 85, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11001101011 supports bitwise reasoning, hexadecimal 66B aligns with computing notation, and the Roman numeral MDCXLIII keeps the encyclopedic tradition alive. These attributes make 1643 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1643 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1638–1648) to tune search ranges, and educators feature 1643 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 1643 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 1643
Is 1643 a prime number?
1643 is composite with 4 total factors and the prime factorization 31 × 53.
What is the prime factorization of 1643?
It breaks down as 31 × 53, multiplying the primes 31 × 53.
How is 1643 represented in binary and hexadecimal?
1643 converts to 11001101011 in binary and 66B in hexadecimal, which are helpful for computer science applications.
Is 1643 a perfect square, cube, or triangular number?
1643 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1643?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.