2160
2160 is a even composite number that follows 2159 and precedes 2161. It is composed of 40 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, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160. Its prime factorization can be written as 2^4 × 3^3 × 5. 2160 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2160 is represented as 100001110000 in binary and 870 in hexadecimal. Historically, it is written as MMCLX in Roman numerals.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3^3 × 5) reveals 8 prime building blocks.
Divisible by 2
2160 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 60 form a multiple of 4.
Divisible by 5
2160 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 9 is a multiple of 9.
Divisible by 10
2160 ends in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 2160 within several notable number theory sequences:
Timeline
Deep dive
How 2160 breaks down
2160 carries 40 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 5280, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100001110000 supports bitwise reasoning, hexadecimal 870 aligns with computing notation, and the Roman numeral MMCLX keeps the encyclopedic tradition alive. These attributes make 2160 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2160 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2155–2165) to tune search ranges, and educators feature 2160 in worksheets about factor trees. Its binary footprint of length 12 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 2160 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 2160
Is 2160 a prime number?
2160 is composite with 40 total factors and the prime factorization 2^4 × 3^3 × 5.
What is the prime factorization of 2160?
It breaks down as 2^4 × 3^3 × 5, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5.
How is 2160 represented in binary and hexadecimal?
2160 converts to 100001110000 in binary and 870 in hexadecimal, which are helpful for computer science applications.
Is 2160 a perfect square, cube, or triangular number?
2160 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2160?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.