4224
4224 is a even composite number that follows 4223 and precedes 4225. It is composed of 32 distinct factors: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 264, 352, 384, 528, 704, 1056, 1408, 2112, 4224. Its prime factorization can be written as 2^7 × 3 × 11. 4224 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4224 is represented as 1000010000000 in binary and 1080 in hexadecimal.
Factor Analysis
32 FactorsProperties
The prime factorization (2^7 × 3 × 11) reveals 9 prime building blocks.
Divisible by 2
4224 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
4224 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 12 is not a multiple of 9.
Divisible by 10
4224 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 4224 within several notable number theory sequences:
Timeline
Deep dive
How 4224 breaks down
4224 carries 32 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 8016, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000010000000 supports bitwise reasoning, hexadecimal 1080 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4224 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4224 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4219–4229) to tune search ranges, and educators feature 4224 in worksheets about factor trees. Its binary footprint of length 13 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 4224 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 4224
Is 4224 a prime number?
4224 is composite with 32 total factors and the prime factorization 2^7 × 3 × 11.
What is the prime factorization of 4224?
It breaks down as 2^7 × 3 × 11, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 11.
How is 4224 represented in binary and hexadecimal?
4224 converts to 1000010000000 in binary and 1080 in hexadecimal, which are helpful for computer science applications.
Is 4224 a perfect square, cube, or triangular number?
4224 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4224?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.