680
680 is a even composite number that follows 679 and precedes 681. It is composed of 16 distinct factors: 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680. Its prime factorization can be written as 2^3 × 5 × 17. 680 is classified as a abundant number based on the sum of its proper divisors. In computer science, 680 is represented as 1010101000 in binary and 2A8 in hexadecimal. Historically, it is written as DCLXXX in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 5 × 17) reveals 5 prime building blocks.
Divisible by 2
680 ends in 0, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
680 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 14 is not a multiple of 9.
Divisible by 10
680 ends in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 680 within several notable number theory sequences:
Timeline
Deep dive
How 680 breaks down
680 carries 16 distinct factors and a digit signature of 14 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 940, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010101000 supports bitwise reasoning, hexadecimal 2A8 aligns with computing notation, and the Roman numeral DCLXXX keeps the encyclopedic tradition alive. These attributes make 680 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 680 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (675–685) to tune search ranges, and educators feature 680 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) help historians, numerologists, and trivia writers tie 680 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 680
Is 680 a prime number?
680 is composite with 16 total factors and the prime factorization 2^3 × 5 × 17.
What is the prime factorization of 680?
It breaks down as 2^3 × 5 × 17, multiplying the primes 2 × 2 × 2 × 5 × 17.
How is 680 represented in binary and hexadecimal?
680 converts to 1010101000 in binary and 2A8 in hexadecimal, which are helpful for computer science applications.
Is 680 a perfect square, cube, or triangular number?
680 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 680?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.