6480
6480 is a even composite number that follows 6479 and precedes 6481. It is composed of 50 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 108, 120, 135, 144, 162, 180, 216, 240, 270, 324, 360, 405, 432, 540, 648, 720, 810, 1080, 1296, 1620, 2160, 3240, 6480. Its prime factorization can be written as 2^4 × 3^4 × 5. 6480 is classified as a abundant number based on the sum of its proper divisors. In computer science, 6480 is represented as 1100101010000 in binary and 1950 in hexadecimal.
Factor Analysis
50 FactorsProperties
The prime factorization (2^4 × 3^4 × 5) reveals 9 prime building blocks.
Divisible by 2
6480 ends in 0, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
6480 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 18 is a multiple of 9.
Divisible by 10
6480 ends in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 6480 within several notable number theory sequences:
Timeline
Deep dive
How 6480 breaks down
6480 carries 50 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 16026, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100101010000 supports bitwise reasoning, hexadecimal 1950 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 6480 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 6480 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (6475–6485) to tune search ranges, and educators feature 6480 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 6480 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 6480
Is 6480 a prime number?
6480 is composite with 50 total factors and the prime factorization 2^4 × 3^4 × 5.
What is the prime factorization of 6480?
It breaks down as 2^4 × 3^4 × 5, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5.
How is 6480 represented in binary and hexadecimal?
6480 converts to 1100101010000 in binary and 1950 in hexadecimal, which are helpful for computer science applications.
Is 6480 a perfect square, cube, or triangular number?
6480 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 6480?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.