9480
9480 is a even composite number that follows 9479 and precedes 9481. It is composed of 32 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 79, 120, 158, 237, 316, 395, 474, 632, 790, 948, 1185, 1580, 1896, 2370, 3160, 4740, 9480. Its prime factorization can be written as 2^3 × 3 × 5 × 79. 9480 is classified as a abundant number based on the sum of its proper divisors. In computer science, 9480 is represented as 10010100001000 in binary and 2508 in hexadecimal.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 5 × 79) reveals 6 prime building blocks.
Divisible by 2
9480 ends in 0, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
9480 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 21 is not a multiple of 9.
Divisible by 10
9480 ends in 0.
Divisible by 11
The alternating digit sum 13 is not a multiple of 11.
Abundant classification and digit analytics place 9480 within several notable number theory sequences:
Timeline
Deep dive
How 9480 breaks down
9480 carries 32 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 19320, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010100001000 supports bitwise reasoning, hexadecimal 2508 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 9480 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 9480 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (9475–9485) to tune search ranges, and educators feature 9480 in worksheets about factor trees. Its binary footprint of length 14 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 9480 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 9480
Is 9480 a prime number?
9480 is composite with 32 total factors and the prime factorization 2^3 × 3 × 5 × 79.
What is the prime factorization of 9480?
It breaks down as 2^3 × 3 × 5 × 79, multiplying the primes 2 × 2 × 2 × 3 × 5 × 79.
How is 9480 represented in binary and hexadecimal?
9480 converts to 10010100001000 in binary and 2508 in hexadecimal, which are helpful for computer science applications.
Is 9480 a perfect square, cube, or triangular number?
9480 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 9480?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.