42408
42408 is a even composite number that follows 42407 and precedes 42409. It is composed of 48 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 31, 36, 38, 57, 62, 72, 76, 93, 114, 124, 152, 171, 186, 228, 248, 279, 342, 372, 456, 558, 589, 684, 744, 1116, 1178, 1368, 1767, 2232, 2356, 3534, 4712, 5301, 7068, 10602, 14136, 21204, 42408. Its prime factorization can be written as 2^3 × 3^2 × 19 × 31. 42408 is classified as a abundant number based on the sum of its proper divisors. In computer science, 42408 is represented as 1010010110101000 in binary and A5A8 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^3 × 3^2 × 19 × 31) reveals 7 prime building blocks.
Divisible by 2
42408 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 08 form a multiple of 4.
Divisible by 5
42408 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
42408 does not end in 0.
Divisible by 11
The alternating digit sum 14 is not a multiple of 11.
Abundant classification and digit analytics place 42408 within several notable number theory sequences:
Timeline
Deep dive
How 42408 breaks down
42408 carries 48 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 82392, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010010110101000 supports bitwise reasoning, hexadecimal A5A8 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 42408 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 42408 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (42403–42413) to tune search ranges, and educators feature 42408 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 42408 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 42408
Is 42408 a prime number?
42408 is composite with 48 total factors and the prime factorization 2^3 × 3^2 × 19 × 31.
What is the prime factorization of 42408?
It breaks down as 2^3 × 3^2 × 19 × 31, multiplying the primes 2 × 2 × 2 × 3 × 3 × 19 × 31.
How is 42408 represented in binary and hexadecimal?
42408 converts to 1010010110101000 in binary and A5A8 in hexadecimal, which are helpful for computer science applications.
Is 42408 a perfect square, cube, or triangular number?
42408 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 42408?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.