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Prime Number

1667

1667 is a odd prime number that follows 1666 and precedes 1668. As a prime number, 1667 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1667. 1667 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1667 is represented as 11010000011 in binary and 683 in hexadecimal. Historically, it is written as MDCLXVII in Roman numerals.

Roman Numeral
MDCLXVII
LatinClassic
Binary
11010000011
Base 2
Hexadecimal
683
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count4
Digit Sum20
Digital Root2
Sum of Factors1668
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

1667 is prime, so its only factors are 1 and 1667.

Canonical form
1667
1667
Divisibility Insights
  • Divisible by 2

    1667 ends in 7, so it is odd.

  • Divisible by 3

    The digit sum 20 is not a multiple of 3.

  • Divisible by 4

    The last two digits 67 are not divisible by 4.

  • Divisible by 5

    1667 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 20 is not a multiple of 9.

  • Divisible by 10

    1667 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 1667 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 1667 breaks down

1667 carries 2 distinct factors and a digit signature of 20 (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 11010000011 supports bitwise reasoning, hexadecimal 683 aligns with computing notation, and the Roman numeral MDCLXVII keeps the encyclopedic tradition alive. These attributes make 1667 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 1667 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (16621672) to tune search ranges, and educators feature 1667 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 1667 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 1667

Is 1667 a prime number?

1667 is prime, meaning it is only divisible by 1 and itself.

What is the prime factorization of 1667?

1667 is already prime, so the factorization is simply 1667.

How is 1667 represented in binary and hexadecimal?

1667 converts to 11010000011 in binary and 683 in hexadecimal, which are helpful for computer science applications.

Is 1667 a perfect square, cube, or triangular number?

1667 is not a perfect square, is not a perfect cube, and is not triangular.

What are the digit sum and digital root of 1667?

The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.