797
797 is a odd prime number that follows 796 and precedes 798. As a prime number, 797 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 797. 797 is classified as a deficient number based on the sum of its proper divisors. In computer science, 797 is represented as 1100011101 in binary and 31D in hexadecimal. Historically, it is written as DCCXCVII in Roman numerals.
Factor Analysis
2 FactorsProperties
797 is prime, so its only factors are 1 and 797.
Divisible by 2
797 ends in 7, so it is odd.
Divisible by 3
The digit sum 23 is not a multiple of 3.
Divisible by 4
The last two digits 97 are not divisible by 4.
Divisible by 5
797 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 23 is not a multiple of 9.
Divisible by 10
797 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 797 within several notable number theory sequences:
Timeline
Deep dive
How 797 breaks down
797 carries 2 distinct factors and a digit signature of 23 (5 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 1100011101 supports bitwise reasoning, hexadecimal 31D aligns with computing notation, and the Roman numeral DCCXCVII keeps the encyclopedic tradition alive. These attributes make 797 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 797 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (792–802) to tune search ranges, and educators feature 797 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 797 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 797
Is 797 a prime number?
797 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 797?
797 is already prime, so the factorization is simply 797.
How is 797 represented in binary and hexadecimal?
797 converts to 1100011101 in binary and 31D in hexadecimal, which are helpful for computer science applications.
Is 797 a perfect square, cube, or triangular number?
797 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 797?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.