4711
4711 is a odd composite number that follows 4710 and precedes 4712. It is composed of 4 distinct factors: 1, 7, 673, 4711. Its prime factorization can be written as 7 × 673. 4711 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4711 is represented as 1001001100111 in binary and 1267 in hexadecimal.
Factor Analysis
4 FactorsProperties
The prime factorization (7 × 673) reveals 2 prime building blocks.
Divisible by 2
4711 ends in 1, so it is odd.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 11 are not divisible by 4.
Divisible by 5
4711 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 13 is not a multiple of 9.
Divisible by 10
4711 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Deficient classification and digit analytics place 4711 within several notable number theory sequences:
Timeline
Deep dive
How 4711 breaks down
4711 carries 4 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 681, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001001100111 supports bitwise reasoning, hexadecimal 1267 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4711 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4711 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4706–4716) to tune search ranges, and educators feature 4711 in worksheets about factor trees. Its binary footprint of length 13 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 4711 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 4711
Is 4711 a prime number?
4711 is composite with 4 total factors and the prime factorization 7 × 673.
What is the prime factorization of 4711?
It breaks down as 7 × 673, multiplying the primes 7 × 673.
How is 4711 represented in binary and hexadecimal?
4711 converts to 1001001100111 in binary and 1267 in hexadecimal, which are helpful for computer science applications.
Is 4711 a perfect square, cube, or triangular number?
4711 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4711?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.