13743
13743 is a odd composite number that follows 13742 and precedes 13744. It is composed of 8 distinct factors: 1, 3, 9, 27, 509, 1527, 4581, 13743. Its prime factorization can be written as 3^3 × 509. 13743 is classified as a deficient number based on the sum of its proper divisors. In computer science, 13743 is represented as 11010110101111 in binary and 35AF in hexadecimal.
Factor Analysis
8 FactorsProperties
The prime factorization (3^3 × 509) reveals 4 prime building blocks.
Divisible by 2
13743 ends in 3, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 43 are not divisible by 4.
Divisible by 5
13743 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 18 is a multiple of 9.
Divisible by 10
13743 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 13743 within several notable number theory sequences:
Timeline
Deep dive
How 13743 breaks down
13743 carries 8 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 6657, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010110101111 supports bitwise reasoning, hexadecimal 35AF aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 13743 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 13743 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (13738–13748) to tune search ranges, and educators feature 13743 in worksheets about factor trees. Its binary footprint of length 14 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 13743 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 13743
Is 13743 a prime number?
13743 is composite with 8 total factors and the prime factorization 3^3 × 509.
What is the prime factorization of 13743?
It breaks down as 3^3 × 509, multiplying the primes 3 × 3 × 3 × 509.
How is 13743 represented in binary and hexadecimal?
13743 converts to 11010110101111 in binary and 35AF in hexadecimal, which are helpful for computer science applications.
Is 13743 a perfect square, cube, or triangular number?
13743 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 13743?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.