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Prime Number

1931

1931 is a odd prime number that follows 1930 and precedes 1932. As a prime number, 1931 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1931. 1931 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1931 is represented as 11110001011 in binary and 78B in hexadecimal. Historically, it is written as MCMXXXI in Roman numerals.

Roman Numeral
MCMXXXI
LatinClassic
Binary
11110001011
Base 2
Hexadecimal
78B
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count4
Digit Sum14
Digital Root5
Sum of Factors1932
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

1931 is prime, so its only factors are 1 and 1931.

Canonical form
1931
1931
Divisibility Insights
  • Divisible by 2

    1931 ends in 1, so it is odd.

  • Divisible by 3

    The digit sum 14 is not a multiple of 3.

  • Divisible by 4

    The last two digits 31 are not divisible by 4.

  • Divisible by 5

    1931 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 14 is not a multiple of 9.

  • Divisible by 10

    1931 does not end in 0.

  • Divisible by 11

    The alternating digit sum -6 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 1931 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 1931 breaks down

1931 carries 2 distinct factors and a digit signature of 14 (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 11110001011 supports bitwise reasoning, hexadecimal 78B aligns with computing notation, and the Roman numeral MCMXXXI keeps the encyclopedic tradition alive. These attributes make 1931 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 1931 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (19261936) to tune search ranges, and educators feature 1931 in worksheets about prime identification. Its binary footprint of length 11 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 1931 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 1931

Is 1931 a prime number?

1931 is prime, meaning it is only divisible by 1 and itself.

What is the prime factorization of 1931?

1931 is already prime, so the factorization is simply 1931.

How is 1931 represented in binary and hexadecimal?

1931 converts to 11110001011 in binary and 78B in hexadecimal, which are helpful for computer science applications.

Is 1931 a perfect square, cube, or triangular number?

1931 is not a perfect square, is not a perfect cube, and is not triangular.

What are the digit sum and digital root of 1931?

The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.