1380
1380 is a even composite number that follows 1379 and precedes 1381. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, 1380. Its prime factorization can be written as 2^2 × 3 × 5 × 23. 1380 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1380 is represented as 10101100100 in binary and 564 in hexadecimal. Historically, it is written as MCCCLXXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 23) reveals 5 prime building blocks.
Divisible by 2
1380 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
1380 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 12 is not a multiple of 9.
Divisible by 10
1380 ends in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 1380 within several notable number theory sequences:
Timeline
Deep dive
How 1380 breaks down
1380 carries 24 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 2652, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10101100100 supports bitwise reasoning, hexadecimal 564 aligns with computing notation, and the Roman numeral MCCCLXXX keeps the encyclopedic tradition alive. These attributes make 1380 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1380 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1375–1385) to tune search ranges, and educators feature 1380 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 1380 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 1380
Is 1380 a prime number?
1380 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5 × 23.
What is the prime factorization of 1380?
It breaks down as 2^2 × 3 × 5 × 23, multiplying the primes 2 × 2 × 3 × 5 × 23.
How is 1380 represented in binary and hexadecimal?
1380 converts to 10101100100 in binary and 564 in hexadecimal, which are helpful for computer science applications.
Is 1380 a perfect square, cube, or triangular number?
1380 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1380?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.