1320
1320 is a even composite number that follows 1319 and precedes 1321. It is composed of 32 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320. Its prime factorization can be written as 2^3 × 3 × 5 × 11. 1320 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1320 is represented as 10100101000 in binary and 528 in hexadecimal. Historically, it is written as MCCCXX in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 5 × 11) reveals 6 prime building blocks.
Divisible by 2
1320 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
1320 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 6 is not a multiple of 9.
Divisible by 10
1320 ends in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 1320 within several notable number theory sequences:
Timeline
Deep dive
How 1320 breaks down
1320 carries 32 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 3000, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100101000 supports bitwise reasoning, hexadecimal 528 aligns with computing notation, and the Roman numeral MCCCXX keeps the encyclopedic tradition alive. These attributes make 1320 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1320 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1315–1325) to tune search ranges, and educators feature 1320 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 1320 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 1320
Is 1320 a prime number?
1320 is composite with 32 total factors and the prime factorization 2^3 × 3 × 5 × 11.
What is the prime factorization of 1320?
It breaks down as 2^3 × 3 × 5 × 11, multiplying the primes 2 × 2 × 2 × 3 × 5 × 11.
How is 1320 represented in binary and hexadecimal?
1320 converts to 10100101000 in binary and 528 in hexadecimal, which are helpful for computer science applications.
Is 1320 a perfect square, cube, or triangular number?
1320 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1320?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.