1780
1780 is a even composite number that follows 1779 and precedes 1781. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780. Its prime factorization can be written as 2^2 × 5 × 89. 1780 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1780 is represented as 11011110100 in binary and 6F4 in hexadecimal. Historically, it is written as MDCCLXXX in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 89) reveals 4 prime building blocks.
Divisible by 2
1780 ends in 0, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
1780 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 16 is not a multiple of 9.
Divisible by 10
1780 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 1780 within several notable number theory sequences:
Timeline
Deep dive
How 1780 breaks down
1780 carries 12 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 2000, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011110100 supports bitwise reasoning, hexadecimal 6F4 aligns with computing notation, and the Roman numeral MDCCLXXX keeps the encyclopedic tradition alive. These attributes make 1780 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1780 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1775–1785) to tune search ranges, and educators feature 1780 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 1780 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 1780
Is 1780 a prime number?
1780 is composite with 12 total factors and the prime factorization 2^2 × 5 × 89.
What is the prime factorization of 1780?
It breaks down as 2^2 × 5 × 89, multiplying the primes 2 × 2 × 5 × 89.
How is 1780 represented in binary and hexadecimal?
1780 converts to 11011110100 in binary and 6F4 in hexadecimal, which are helpful for computer science applications.
Is 1780 a perfect square, cube, or triangular number?
1780 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1780?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.