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Prime Number

8221

8221 is a odd prime number that follows 8220 and precedes 8222. As a prime number, 8221 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 8221. 8221 is classified as a deficient number based on the sum of its proper divisors. In computer science, 8221 is represented as 10000000011101 in binary and 201D in hexadecimal.

Roman Numeral
N/A (1-3999)
LatinClassic
Binary
10000000011101
Base 2
Hexadecimal
201D
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count4
Digit Sum13
Digital Root4
Sum of Factors8222
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

8221 is prime, so its only factors are 1 and 8221.

Canonical form
8221
8221
Divisibility Insights
  • Divisible by 2

    8221 ends in 1, so it is odd.

  • Divisible by 3

    The digit sum 13 is not a multiple of 3.

  • Divisible by 4

    The last two digits 21 are not divisible by 4.

  • Divisible by 5

    8221 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 13 is not a multiple of 9.

  • Divisible by 10

    8221 does not end in 0.

  • Divisible by 11

    The alternating digit sum 7 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 8221 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 8221 breaks down

8221 carries 2 distinct factors and a digit signature of 13 (4 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 10000000011101 supports bitwise reasoning, hexadecimal 201D aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8221 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 8221 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (82168226) to tune search ranges, and educators feature 8221 in worksheets about prime identification. Its binary footprint of length 14 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 8221 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 8221

Is 8221 a prime number?

8221 is prime, meaning it is only divisible by 1 and itself.

What is the prime factorization of 8221?

8221 is already prime, so the factorization is simply 8221.

How is 8221 represented in binary and hexadecimal?

8221 converts to 10000000011101 in binary and 201D in hexadecimal, which are helpful for computer science applications.

Is 8221 a perfect square, cube, or triangular number?

8221 is not a perfect square, is not a perfect cube, and is not triangular.

What are the digit sum and digital root of 8221?

The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.