311
311 is a odd prime number that follows 310 and precedes 312. As a prime number, 311 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 311. 311 is classified as a deficient number based on the sum of its proper divisors. In computer science, 311 is represented as 100110111 in binary and 137 in hexadecimal. Historically, it is written as CCCXI in Roman numerals.
Factor Analysis
2 FactorsProperties
311 is prime, so its only factors are 1 and 311.
Divisible by 2
311 ends in 1, so it is odd.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 11 are not divisible by 4.
Divisible by 5
311 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 5 is not a multiple of 9.
Divisible by 10
311 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 311 within several notable number theory sequences:
Timeline
Deep dive
How 311 breaks down
311 carries 2 distinct factors and a digit signature of 5 (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 100110111 supports bitwise reasoning, hexadecimal 137 aligns with computing notation, and the Roman numeral CCCXI keeps the encyclopedic tradition alive. These attributes make 311 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 311 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (306–316) to tune search ranges, and educators feature 311 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 311 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 311
Is 311 a prime number?
311 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 311?
311 is already prime, so the factorization is simply 311.
How is 311 represented in binary and hexadecimal?
311 converts to 100110111 in binary and 137 in hexadecimal, which are helpful for computer science applications.
Is 311 a perfect square, cube, or triangular number?
311 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 311?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.