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Prime Number

1721

1721 is a odd prime number that follows 1720 and precedes 1722. As a prime number, 1721 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1721. 1721 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1721 is represented as 11010111001 in binary and 6B9 in hexadecimal. Historically, it is written as MDCCXXI in Roman numerals.

Roman Numeral
MDCCXXI
LatinClassic
Binary
11010111001
Base 2
Hexadecimal
6B9
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count4
Digit Sum11
Digital Root2
Sum of Factors1722
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

1721 is prime, so its only factors are 1 and 1721.

Canonical form
1721
1721
Divisibility Insights
  • Divisible by 2

    1721 ends in 1, so it is odd.

  • Divisible by 3

    The digit sum 11 is not a multiple of 3.

  • Divisible by 4

    The last two digits 21 are not divisible by 4.

  • Divisible by 5

    1721 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 11 is not a multiple of 9.

  • Divisible by 10

    1721 does not end in 0.

  • Divisible by 11

    The alternating digit sum -5 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 1721 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 1721 breaks down

1721 carries 2 distinct factors and a digit signature of 11 (2 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 11010111001 supports bitwise reasoning, hexadecimal 6B9 aligns with computing notation, and the Roman numeral MDCCXXI keeps the encyclopedic tradition alive. These attributes make 1721 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 1721 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (17161726) to tune search ranges, and educators feature 1721 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 1721 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 1721

Is 1721 a prime number?

1721 is prime, meaning it is only divisible by 1 and itself.

What is the prime factorization of 1721?

1721 is already prime, so the factorization is simply 1721.

How is 1721 represented in binary and hexadecimal?

1721 converts to 11010111001 in binary and 6B9 in hexadecimal, which are helpful for computer science applications.

Is 1721 a perfect square, cube, or triangular number?

1721 is not a perfect square, is not a perfect cube, and is not triangular.

What are the digit sum and digital root of 1721?

The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.