9180
9180 is a even composite number that follows 9179 and precedes 9181. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34, 36, 45, 51, 54, 60, 68, 85, 90, 102, 108, 135, 153, 170, 180, 204, 255, 270, 306, 340, 459, 510, 540, 612, 765, 918, 1020, 1530, 1836, 2295, 3060, 4590, 9180. Its prime factorization can be written as 2^2 × 3^3 × 5 × 17. 9180 is classified as a abundant number based on the sum of its proper divisors. In computer science, 9180 is represented as 10001111011100 in binary and 23DC in hexadecimal. It also belongs to the triangular number sequence.
Factor Analysis
48 FactorsProperties
The prime factorization (2^2 × 3^3 × 5 × 17) reveals 7 prime building blocks.
Divisible by 2
9180 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
9180 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
9180 ends in 0.
Divisible by 11
The alternating digit sum 16 is not a multiple of 11.
Abundant classification and digit analytics place 9180 within several notable number theory sequences:
Timeline
Deep dive
How 9180 breaks down
9180 carries 48 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 21060, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001111011100 supports bitwise reasoning, hexadecimal 23DC aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 9180 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 9180 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (9175–9185) to tune search ranges, and educators feature 9180 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, Triangular numbers) help historians, numerologists, and trivia writers tie 9180 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 9180
Is 9180 a prime number?
9180 is composite with 48 total factors and the prime factorization 2^2 × 3^3 × 5 × 17.
What is the prime factorization of 9180?
It breaks down as 2^2 × 3^3 × 5 × 17, multiplying the primes 2 × 2 × 3 × 3 × 3 × 5 × 17.
How is 9180 represented in binary and hexadecimal?
9180 converts to 10001111011100 in binary and 23DC in hexadecimal, which are helpful for computer science applications.
Is 9180 a perfect square, cube, or triangular number?
9180 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 9180?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.