1080
1080 is a even composite number that follows 1079 and precedes 1081. It is composed of 32 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080. Its prime factorization can be written as 2^3 × 3^3 × 5. 1080 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1080 is represented as 10000111000 in binary and 438 in hexadecimal. Historically, it is written as MLXXX in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3^3 × 5) reveals 7 prime building blocks.
Divisible by 2
1080 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 80 form a multiple of 4.
Divisible by 5
1080 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
1080 ends in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 1080 within several notable number theory sequences:
Timeline
Deep dive
How 1080 breaks down
1080 carries 32 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2520, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000111000 supports bitwise reasoning, hexadecimal 438 aligns with computing notation, and the Roman numeral MLXXX keeps the encyclopedic tradition alive. These attributes make 1080 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1080 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1075–1085) to tune search ranges, and educators feature 1080 in worksheets about factor trees. Its binary footprint of length 11 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 1080 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 1080
Is 1080 a prime number?
1080 is composite with 32 total factors and the prime factorization 2^3 × 3^3 × 5.
What is the prime factorization of 1080?
It breaks down as 2^3 × 3^3 × 5, multiplying the primes 2 × 2 × 2 × 3 × 3 × 3 × 5.
How is 1080 represented in binary and hexadecimal?
1080 converts to 10000111000 in binary and 438 in hexadecimal, which are helpful for computer science applications.
Is 1080 a perfect square, cube, or triangular number?
1080 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1080?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.