42048
42048 is a even composite number that follows 42047 and precedes 42049. It is composed of 42 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 73, 96, 144, 146, 192, 219, 288, 292, 438, 576, 584, 657, 876, 1168, 1314, 1752, 2336, 2628, 3504, 4672, 5256, 7008, 10512, 14016, 21024, 42048. Its prime factorization can be written as 2^6 × 3^2 × 73. 42048 is classified as a abundant number based on the sum of its proper divisors. In computer science, 42048 is represented as 1010010001000000 in binary and A440 in hexadecimal.
Factor Analysis
42 FactorsProperties
The prime factorization (2^6 × 3^2 × 73) reveals 9 prime building blocks.
Divisible by 2
42048 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
42048 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
42048 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 42048 within several notable number theory sequences:
Timeline
Deep dive
How 42048 breaks down
42048 carries 42 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 80126, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010010001000000 supports bitwise reasoning, hexadecimal A440 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 42048 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 42048 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (42043–42053) to tune search ranges, and educators feature 42048 in worksheets about factor trees. Its binary footprint of length 16 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 42048 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 42048
Is 42048 a prime number?
42048 is composite with 42 total factors and the prime factorization 2^6 × 3^2 × 73.
What is the prime factorization of 42048?
It breaks down as 2^6 × 3^2 × 73, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 73.
How is 42048 represented in binary and hexadecimal?
42048 converts to 1010010001000000 in binary and A440 in hexadecimal, which are helpful for computer science applications.
Is 42048 a perfect square, cube, or triangular number?
42048 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 42048?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.