4096
4096 is a even composite number that follows 4095 and precedes 4097. It is composed of 13 distinct factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096. Its prime factorization can be written as 2^12. 4096 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4096 is represented as 1000000000000 in binary and 1000 in hexadecimal. It also belongs to the perfect square, perfect cube sequences.
Factor Analysis
13 FactorsProperties
The prime factorization (2^12) reveals 12 prime building blocks.
Divisible by 2
4096 ends in 6, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 96 form a multiple of 4.
Divisible by 5
4096 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 19 is not a multiple of 9.
Divisible by 10
4096 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Deficient classification and digit analytics place 4096 within several notable number theory sequences:
Timeline
Deep dive
How 4096 breaks down
4096 carries 13 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 4095, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000000000000 supports bitwise reasoning, hexadecimal 1000 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4096 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4096 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4091–4101) to tune search ranges, and educators feature 4096 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, Perfect squares, Perfect cubes) help historians, numerologists, and trivia writers tie 4096 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 4096
Is 4096 a prime number?
4096 is composite with 13 total factors and the prime factorization 2^12.
What is the prime factorization of 4096?
It breaks down as 2^12, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
How is 4096 represented in binary and hexadecimal?
4096 converts to 1000000000000 in binary and 1000 in hexadecimal, which are helpful for computer science applications.
Is 4096 a perfect square, cube, or triangular number?
4096 is a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 4096?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.