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Prime Number

67

67 is a odd prime number that follows 66 and precedes 68. As a prime number, 67 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 67. 67 is classified as a deficient number based on the sum of its proper divisors. In computer science, 67 is represented as 1000011 in binary and 43 in hexadecimal. Historically, it is written as LXVII in Roman numerals.

Roman Numeral
LXVII
LatinClassic
Binary
1000011
Base 2
Hexadecimal
43
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count2
Digit Sum13
Digital Root4
Sum of Factors68
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

67 is prime, so its only factors are 1 and 67.

Canonical form
67
67
Divisibility Insights
  • Divisible by 2

    67 ends in 7, so it is odd.

  • Divisible by 3

    The digit sum 13 is not a multiple of 3.

  • Divisible by 4

    The last two digits 67 are not divisible by 4.

  • Divisible by 5

    67 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

    67 does not end in 0.

  • Divisible by 11

    The alternating digit sum -1 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 67 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 67 breaks down

67 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 1000011 supports bitwise reasoning, hexadecimal 43 aligns with computing notation, and the Roman numeral LXVII keeps the encyclopedic tradition alive. These attributes make 67 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 67 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (6272) to tune search ranges, and educators feature 67 in worksheets about prime identification. Its binary footprint of length 7 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 67 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 67

Is 67 a prime number?

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

What is the prime factorization of 67?

67 is already prime, so the factorization is simply 67.

How is 67 represented in binary and hexadecimal?

67 converts to 1000011 in binary and 43 in hexadecimal, which are helpful for computer science applications.

Is 67 a perfect square, cube, or triangular number?

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

What are the digit sum and digital root of 67?

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