24768
24768 is a even composite number that follows 24767 and precedes 24769. It is composed of 42 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 43, 48, 64, 72, 86, 96, 129, 144, 172, 192, 258, 288, 344, 387, 516, 576, 688, 774, 1032, 1376, 1548, 2064, 2752, 3096, 4128, 6192, 8256, 12384, 24768. Its prime factorization can be written as 2^6 × 3^2 × 43. 24768 is classified as a abundant number based on the sum of its proper divisors. In computer science, 24768 is represented as 110000011000000 in binary and 60C0 in hexadecimal.
Factor Analysis
42 FactorsProperties
The prime factorization (2^6 × 3^2 × 43) reveals 9 prime building blocks.
Divisible by 2
24768 ends in 8, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
24768 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 27 is a multiple of 9.
Divisible by 10
24768 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 24768 within several notable number theory sequences:
Timeline
Deep dive
How 24768 breaks down
24768 carries 42 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 47876, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110000011000000 supports bitwise reasoning, hexadecimal 60C0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 24768 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 24768 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (24763–24773) to tune search ranges, and educators feature 24768 in worksheets about factor trees. Its binary footprint of length 15 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 24768 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 24768
Is 24768 a prime number?
24768 is composite with 42 total factors and the prime factorization 2^6 × 3^2 × 43.
What is the prime factorization of 24768?
It breaks down as 2^6 × 3^2 × 43, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 43.
How is 24768 represented in binary and hexadecimal?
24768 converts to 110000011000000 in binary and 60C0 in hexadecimal, which are helpful for computer science applications.
Is 24768 a perfect square, cube, or triangular number?
24768 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 24768?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.