681
681 is a odd composite number that follows 680 and precedes 682. It is composed of 4 distinct factors: 1, 3, 227, 681. Its prime factorization can be written as 3 × 227. 681 is classified as a deficient number based on the sum of its proper divisors. In computer science, 681 is represented as 1010101001 in binary and 2A9 in hexadecimal. Historically, it is written as DCLXXXI in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 227) reveals 2 prime building blocks.
Divisible by 2
681 ends in 1, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 81 are not divisible by 4.
Divisible by 5
681 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 15 is not a multiple of 9.
Divisible by 10
681 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 681 within several notable number theory sequences:
Timeline
Deep dive
How 681 breaks down
681 carries 4 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 231, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010101001 supports bitwise reasoning, hexadecimal 2A9 aligns with computing notation, and the Roman numeral DCLXXXI keeps the encyclopedic tradition alive. These attributes make 681 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 681 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (676–686) to tune search ranges, and educators feature 681 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, Deficient numbers) help historians, numerologists, and trivia writers tie 681 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 681
Is 681 a prime number?
681 is composite with 4 total factors and the prime factorization 3 × 227.
What is the prime factorization of 681?
It breaks down as 3 × 227, multiplying the primes 3 × 227.
How is 681 represented in binary and hexadecimal?
681 converts to 1010101001 in binary and 2A9 in hexadecimal, which are helpful for computer science applications.
Is 681 a perfect square, cube, or triangular number?
681 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 681?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.