4095
4095 is a odd composite number that follows 4094 and precedes 4096. It is composed of 24 distinct factors: 1, 3, 5, 7, 9, 13, 15, 21, 35, 39, 45, 63, 65, 91, 105, 117, 195, 273, 315, 455, 585, 819, 1365, 4095. Its prime factorization can be written as 3^2 × 5 × 7 × 13. 4095 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4095 is represented as 111111111111 in binary and FFF in hexadecimal. It also belongs to the triangular number sequence.
Factor Analysis
24 FactorsProperties
The prime factorization (3^2 × 5 × 7 × 13) reveals 5 prime building blocks.
Divisible by 2
4095 ends in 5, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 95 are not divisible by 4.
Divisible by 5
4095 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 18 is a multiple of 9.
Divisible by 10
4095 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 4095 within several notable number theory sequences:
Timeline
Deep dive
How 4095 breaks down
4095 carries 24 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4641, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111111111 supports bitwise reasoning, hexadecimal FFF aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4095 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4095 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4090–4100) to tune search ranges, and educators feature 4095 in worksheets about factor trees. Its binary footprint of length 12 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 4095 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 4095
Is 4095 a prime number?
4095 is composite with 24 total factors and the prime factorization 3^2 × 5 × 7 × 13.
What is the prime factorization of 4095?
It breaks down as 3^2 × 5 × 7 × 13, multiplying the primes 3 × 3 × 5 × 7 × 13.
How is 4095 represented in binary and hexadecimal?
4095 converts to 111111111111 in binary and FFF in hexadecimal, which are helpful for computer science applications.
Is 4095 a perfect square, cube, or triangular number?
4095 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 4095?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.