38688
38688 is a even composite number that follows 38687 and precedes 38689. It is composed of 48 distinct factors: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52, 62, 78, 93, 96, 104, 124, 156, 186, 208, 248, 312, 372, 403, 416, 496, 624, 744, 806, 992, 1209, 1248, 1488, 1612, 2418, 2976, 3224, 4836, 6448, 9672, 12896, 19344, 38688. Its prime factorization can be written as 2^5 × 3 × 13 × 31. 38688 is classified as a abundant number based on the sum of its proper divisors. In computer science, 38688 is represented as 1001011100100000 in binary and 9720 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^5 × 3 × 13 × 31) reveals 8 prime building blocks.
Divisible by 2
38688 ends in 8, so it is even.
Divisible by 3
The digit sum 33 is a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
38688 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 33 is not a multiple of 9.
Divisible by 10
38688 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 38688 within several notable number theory sequences:
Timeline
Deep dive
How 38688 breaks down
38688 carries 48 distinct factors and a digit signature of 33 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 74208, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001011100100000 supports bitwise reasoning, hexadecimal 9720 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 38688 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 38688 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (38683–38693) to tune search ranges, and educators feature 38688 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 38688 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 38688
Is 38688 a prime number?
38688 is composite with 48 total factors and the prime factorization 2^5 × 3 × 13 × 31.
What is the prime factorization of 38688?
It breaks down as 2^5 × 3 × 13 × 31, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 13 × 31.
How is 38688 represented in binary and hexadecimal?
38688 converts to 1001011100100000 in binary and 9720 in hexadecimal, which are helpful for computer science applications.
Is 38688 a perfect square, cube, or triangular number?
38688 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 38688?
The digits sum to 33, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.