4480
4480 is a even composite number that follows 4479 and precedes 4481. It is composed of 32 distinct factors: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 280, 320, 448, 560, 640, 896, 1120, 2240, 4480. Its prime factorization can be written as 2^7 × 5 × 7. 4480 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4480 is represented as 1000110000000 in binary and 1180 in hexadecimal.
Factor Analysis
32 FactorsProperties
The prime factorization (2^7 × 5 × 7) reveals 9 prime building blocks.
Divisible by 2
4480 ends in 0, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
4480 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 16 is not a multiple of 9.
Divisible by 10
4480 ends in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 4480 within several notable number theory sequences:
Timeline
Deep dive
How 4480 breaks down
4480 carries 32 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 7760, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000110000000 supports bitwise reasoning, hexadecimal 1180 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4480 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4480 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4475–4485) to tune search ranges, and educators feature 4480 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 4480 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 4480
Is 4480 a prime number?
4480 is composite with 32 total factors and the prime factorization 2^7 × 5 × 7.
What is the prime factorization of 4480?
It breaks down as 2^7 × 5 × 7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 7.
How is 4480 represented in binary and hexadecimal?
4480 converts to 1000110000000 in binary and 1180 in hexadecimal, which are helpful for computer science applications.
Is 4480 a perfect square, cube, or triangular number?
4480 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4480?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.