480
480 is a even composite number that follows 479 and precedes 481. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480. Its prime factorization can be written as 2^5 × 3 × 5. 480 is classified as a abundant number based on the sum of its proper divisors. In computer science, 480 is represented as 111100000 in binary and 1E0 in hexadecimal. Historically, it is written as CDLXXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 3 × 5) reveals 7 prime building blocks.
Divisible by 2
480 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
480 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 12 is not a multiple of 9.
Divisible by 10
480 ends in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 480 within several notable number theory sequences:
Timeline
Deep dive
How 480 breaks down
480 carries 24 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1032, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111100000 supports bitwise reasoning, hexadecimal 1E0 aligns with computing notation, and the Roman numeral CDLXXX keeps the encyclopedic tradition alive. These attributes make 480 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 480 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (475–485) to tune search ranges, and educators feature 480 in worksheets about factor trees. Its binary footprint of length 9 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 480 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 480
Is 480 a prime number?
480 is composite with 24 total factors and the prime factorization 2^5 × 3 × 5.
What is the prime factorization of 480?
It breaks down as 2^5 × 3 × 5, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 5.
How is 480 represented in binary and hexadecimal?
480 converts to 111100000 in binary and 1E0 in hexadecimal, which are helpful for computer science applications.
Is 480 a perfect square, cube, or triangular number?
480 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 480?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.