317
317 is a odd prime number that follows 316 and precedes 318. As a prime number, 317 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 317. 317 is classified as a deficient number based on the sum of its proper divisors. In computer science, 317 is represented as 100111101 in binary and 13D in hexadecimal. Historically, it is written as CCCXVII in Roman numerals.
Factor Analysis
2 FactorsProperties
317 is prime, so its only factors are 1 and 317.
Divisible by 2
317 ends in 7, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 17 are not divisible by 4.
Divisible by 5
317 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 11 is not a multiple of 9.
Divisible by 10
317 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Deficient classification and digit analytics place 317 within several notable number theory sequences:
Timeline
Deep dive
How 317 breaks down
317 carries 2 distinct factors and a digit signature of 11 (2 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 100111101 supports bitwise reasoning, hexadecimal 13D aligns with computing notation, and the Roman numeral CCCXVII keeps the encyclopedic tradition alive. These attributes make 317 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 317 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (312–322) to tune search ranges, and educators feature 317 in worksheets about prime identification. Its binary footprint of length 9 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 317 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 317
Is 317 a prime number?
317 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 317?
317 is already prime, so the factorization is simply 317.
How is 317 represented in binary and hexadecimal?
317 converts to 100111101 in binary and 13D in hexadecimal, which are helpful for computer science applications.
Is 317 a perfect square, cube, or triangular number?
317 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 317?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.