691
691 is a odd prime number that follows 690 and precedes 692. As a prime number, 691 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 691. 691 is classified as a deficient number based on the sum of its proper divisors. In computer science, 691 is represented as 1010110011 in binary and 2B3 in hexadecimal. Historically, it is written as DCXCI in Roman numerals.
Factor Analysis
2 FactorsProperties
691 is prime, so its only factors are 1 and 691.
Divisible by 2
691 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 91 are not divisible by 4.
Divisible by 5
691 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
691 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 691 within several notable number theory sequences:
Timeline
Deep dive
How 691 breaks down
691 carries 2 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010110011 supports bitwise reasoning, hexadecimal 2B3 aligns with computing notation, and the Roman numeral DCXCI keeps the encyclopedic tradition alive. These attributes make 691 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 691 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (686–696) to tune search ranges, and educators feature 691 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 691 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 691
Is 691 a prime number?
691 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 691?
691 is already prime, so the factorization is simply 691.
How is 691 represented in binary and hexadecimal?
691 converts to 1010110011 in binary and 2B3 in hexadecimal, which are helpful for computer science applications.
Is 691 a perfect square, cube, or triangular number?
691 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 691?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.