4048
4048 is a even composite number that follows 4047 and precedes 4049. It is composed of 20 distinct factors: 1, 2, 4, 8, 11, 16, 22, 23, 44, 46, 88, 92, 176, 184, 253, 368, 506, 1012, 2024, 4048. Its prime factorization can be written as 2^4 × 11 × 23. 4048 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4048 is represented as 111111010000 in binary and FD0 in hexadecimal.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 11 × 23) reveals 6 prime building blocks.
Divisible by 2
4048 ends in 8, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
4048 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 16 is not a multiple of 9.
Divisible by 10
4048 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 4048 within several notable number theory sequences:
Timeline
Deep dive
How 4048 breaks down
4048 carries 20 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 4880, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111010000 supports bitwise reasoning, hexadecimal FD0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4048 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4048 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4043–4053) to tune search ranges, and educators feature 4048 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) help historians, numerologists, and trivia writers tie 4048 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 4048
Is 4048 a prime number?
4048 is composite with 20 total factors and the prime factorization 2^4 × 11 × 23.
What is the prime factorization of 4048?
It breaks down as 2^4 × 11 × 23, multiplying the primes 2 × 2 × 2 × 2 × 11 × 23.
How is 4048 represented in binary and hexadecimal?
4048 converts to 111111010000 in binary and FD0 in hexadecimal, which are helpful for computer science applications.
Is 4048 a perfect square, cube, or triangular number?
4048 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4048?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.