1681
1681 is a odd composite number that follows 1680 and precedes 1682. It is composed of 3 distinct factors: 1, 41, 1681. Its prime factorization can be written as 41^2. 1681 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1681 is represented as 11010010001 in binary and 691 in hexadecimal. Historically, it is written as MDCLXXXI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
3 FactorsProperties
The prime factorization (41^2) reveals 2 prime building blocks.
Divisible by 2
1681 ends in 1, so it is odd.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 81 are not divisible by 4.
Divisible by 5
1681 does not end in 0 or 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
1681 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 1681 within several notable number theory sequences:
Timeline
Deep dive
How 1681 breaks down
1681 carries 3 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 42, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010010001 supports bitwise reasoning, hexadecimal 691 aligns with computing notation, and the Roman numeral MDCLXXXI keeps the encyclopedic tradition alive. These attributes make 1681 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1681 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1676–1686) to tune search ranges, and educators feature 1681 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, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 1681 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 1681
Is 1681 a prime number?
1681 is composite with 3 total factors and the prime factorization 41^2.
What is the prime factorization of 1681?
It breaks down as 41^2, multiplying the primes 41 × 41.
How is 1681 represented in binary and hexadecimal?
1681 converts to 11010010001 in binary and 691 in hexadecimal, which are helpful for computer science applications.
Is 1681 a perfect square, cube, or triangular number?
1681 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1681?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.