313
313 is a odd prime number that follows 312 and precedes 314. As a prime number, 313 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 313. 313 is classified as a deficient number based on the sum of its proper divisors. In computer science, 313 is represented as 100111001 in binary and 139 in hexadecimal. Historically, it is written as CCCXIII in Roman numerals.
Factor Analysis
2 FactorsProperties
313 is prime, so its only factors are 1 and 313.
Divisible by 2
313 ends in 3, so it is odd.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
313 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 7 is not a multiple of 9.
Divisible by 10
313 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 313 within several notable number theory sequences:
Timeline
Deep dive
How 313 breaks down
313 carries 2 distinct factors and a digit signature of 7 (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 100111001 supports bitwise reasoning, hexadecimal 139 aligns with computing notation, and the Roman numeral CCCXIII keeps the encyclopedic tradition alive. These attributes make 313 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 313 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (308–318) to tune search ranges, and educators feature 313 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 313 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 313
Is 313 a prime number?
313 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 313?
313 is already prime, so the factorization is simply 313.
How is 313 represented in binary and hexadecimal?
313 converts to 100111001 in binary and 139 in hexadecimal, which are helpful for computer science applications.
Is 313 a perfect square, cube, or triangular number?
313 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 313?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.