1680
1680 is a even composite number that follows 1679 and precedes 1681. It is composed of 40 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680. Its prime factorization can be written as 2^4 × 3 × 5 × 7. 1680 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1680 is represented as 11010010000 in binary and 690 in hexadecimal. Historically, it is written as MDCLXXX in Roman numerals.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3 × 5 × 7) reveals 7 prime building blocks.
Divisible by 2
1680 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
1680 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
1680 ends in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 1680 within several notable number theory sequences:
Timeline
Deep dive
How 1680 breaks down
1680 carries 40 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 4272, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010010000 supports bitwise reasoning, hexadecimal 690 aligns with computing notation, and the Roman numeral MDCLXXX keeps the encyclopedic tradition alive. These attributes make 1680 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1680 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1675–1685) to tune search ranges, and educators feature 1680 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 1680 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 1680
Is 1680 a prime number?
1680 is composite with 40 total factors and the prime factorization 2^4 × 3 × 5 × 7.
What is the prime factorization of 1680?
It breaks down as 2^4 × 3 × 5 × 7, multiplying the primes 2 × 2 × 2 × 2 × 3 × 5 × 7.
How is 1680 represented in binary and hexadecimal?
1680 converts to 11010010000 in binary and 690 in hexadecimal, which are helpful for computer science applications.
Is 1680 a perfect square, cube, or triangular number?
1680 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1680?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.