67824
67824 is a even composite number that follows 67823 and precedes 67825. It is composed of 40 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 157, 216, 314, 432, 471, 628, 942, 1256, 1413, 1884, 2512, 2826, 3768, 4239, 5652, 7536, 8478, 11304, 16956, 22608, 33912, 67824. Its prime factorization can be written as 2^4 × 3^3 × 157. 67824 is classified as a abundant number based on the sum of its proper divisors. In computer science, 67824 is represented as 10000100011110000 in binary and 108F0 in hexadecimal.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3^3 × 157) reveals 8 prime building blocks.
Divisible by 2
67824 ends in 4, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
67824 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
67824 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 67824 within several notable number theory sequences:
Timeline
Deep dive
How 67824 breaks down
67824 carries 40 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 128096, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000100011110000 supports bitwise reasoning, hexadecimal 108F0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 67824 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 67824 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (67819–67829) to tune search ranges, and educators feature 67824 in worksheets about factor trees. Its binary footprint of length 17 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 67824 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 67824
Is 67824 a prime number?
67824 is composite with 40 total factors and the prime factorization 2^4 × 3^3 × 157.
What is the prime factorization of 67824?
It breaks down as 2^4 × 3^3 × 157, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 157.
How is 67824 represented in binary and hexadecimal?
67824 converts to 10000100011110000 in binary and 108F0 in hexadecimal, which are helpful for computer science applications.
Is 67824 a perfect square, cube, or triangular number?
67824 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 67824?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.