780
780 is a even composite number that follows 779 and precedes 781. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780. Its prime factorization can be written as 2^2 × 3 × 5 × 13. 780 is classified as a abundant number based on the sum of its proper divisors. In computer science, 780 is represented as 1100001100 in binary and 30C in hexadecimal. Historically, it is written as DCCLXXX in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 13) reveals 5 prime building blocks.
Divisible by 2
780 ends in 0, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
780 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 15 is not a multiple of 9.
Divisible by 10
780 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 780 within several notable number theory sequences:
Timeline
Deep dive
How 780 breaks down
780 carries 24 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 1572, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100001100 supports bitwise reasoning, hexadecimal 30C aligns with computing notation, and the Roman numeral DCCLXXX keeps the encyclopedic tradition alive. These attributes make 780 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 780 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (775–785) to tune search ranges, and educators feature 780 in worksheets about factor trees. Its binary footprint of length 10 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 780 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 780
Is 780 a prime number?
780 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5 × 13.
What is the prime factorization of 780?
It breaks down as 2^2 × 3 × 5 × 13, multiplying the primes 2 × 2 × 3 × 5 × 13.
How is 780 represented in binary and hexadecimal?
780 converts to 1100001100 in binary and 30C in hexadecimal, which are helpful for computer science applications.
Is 780 a perfect square, cube, or triangular number?
780 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 780?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.