4320
4320 is a even composite number that follows 4319 and precedes 4321. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160, 4320. Its prime factorization can be written as 2^5 × 3^3 × 5. 4320 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4320 is represented as 1000011100000 in binary and 10E0 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^5 × 3^3 × 5) reveals 9 prime building blocks.
Divisible by 2
4320 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
4320 ends in 0, so it is divisible by 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
4320 ends in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 4320 within several notable number theory sequences:
Timeline
Deep dive
How 4320 breaks down
4320 carries 48 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 10800, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000011100000 supports bitwise reasoning, hexadecimal 10E0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4320 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4320 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4315–4325) to tune search ranges, and educators feature 4320 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 4320 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 4320
Is 4320 a prime number?
4320 is composite with 48 total factors and the prime factorization 2^5 × 3^3 × 5.
What is the prime factorization of 4320?
It breaks down as 2^5 × 3^3 × 5, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5.
How is 4320 represented in binary and hexadecimal?
4320 converts to 1000011100000 in binary and 10E0 in hexadecimal, which are helpful for computer science applications.
Is 4320 a perfect square, cube, or triangular number?
4320 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4320?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.