3024
3024 is a even composite number that follows 3023 and precedes 3025. It is composed of 40 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 84, 108, 112, 126, 144, 168, 189, 216, 252, 336, 378, 432, 504, 756, 1008, 1512, 3024. Its prime factorization can be written as 2^4 × 3^3 × 7. 3024 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3024 is represented as 101111010000 in binary and BD0 in hexadecimal. Historically, it is written as MMMXXIV in Roman numerals.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3^3 × 7) reveals 8 prime building blocks.
Divisible by 2
3024 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
3024 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 9 is a multiple of 9.
Divisible by 10
3024 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 3024 within several notable number theory sequences:
Timeline
Deep dive
How 3024 breaks down
3024 carries 40 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 6896, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101111010000 supports bitwise reasoning, hexadecimal BD0 aligns with computing notation, and the Roman numeral MMMXXIV keeps the encyclopedic tradition alive. These attributes make 3024 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3024 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3019–3029) to tune search ranges, and educators feature 3024 in worksheets about factor trees. Its binary footprint of length 12 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 3024 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 3024
Is 3024 a prime number?
3024 is composite with 40 total factors and the prime factorization 2^4 × 3^3 × 7.
What is the prime factorization of 3024?
It breaks down as 2^4 × 3^3 × 7, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7.
How is 3024 represented in binary and hexadecimal?
3024 converts to 101111010000 in binary and BD0 in hexadecimal, which are helpful for computer science applications.
Is 3024 a perfect square, cube, or triangular number?
3024 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3024?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.