331
331 is a odd prime number that follows 330 and precedes 332. As a prime number, 331 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 331. 331 is classified as a deficient number based on the sum of its proper divisors. In computer science, 331 is represented as 101001011 in binary and 14B in hexadecimal. Historically, it is written as CCCXXXI in Roman numerals.
Factor Analysis
2 FactorsProperties
331 is prime, so its only factors are 1 and 331.
Divisible by 2
331 ends in 1, so it is odd.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 31 are not divisible by 4.
Divisible by 5
331 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
331 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Deficient classification and digit analytics place 331 within several notable number theory sequences:
Timeline
Deep dive
How 331 breaks down
331 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 101001011 supports bitwise reasoning, hexadecimal 14B aligns with computing notation, and the Roman numeral CCCXXXI keeps the encyclopedic tradition alive. These attributes make 331 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 331 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (326–336) to tune search ranges, and educators feature 331 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 331 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 331
Is 331 a prime number?
331 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 331?
331 is already prime, so the factorization is simply 331.
How is 331 represented in binary and hexadecimal?
331 converts to 101001011 in binary and 14B in hexadecimal, which are helpful for computer science applications.
Is 331 a perfect square, cube, or triangular number?
331 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 331?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.