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Prime Number

167

167 is a odd prime number that follows 166 and precedes 168. As a prime number, 167 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 167. 167 is classified as a deficient number based on the sum of its proper divisors. In computer science, 167 is represented as 10100111 in binary and A7 in hexadecimal. Historically, it is written as CLXVII in Roman numerals.

Roman Numeral
CLXVII
LatinClassic
Binary
10100111
Base 2
Hexadecimal
A7
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count3
Digit Sum14
Digital Root5
Sum of Factors168
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

167 is prime, so its only factors are 1 and 167.

Canonical form
167
167
Divisibility Insights
  • Divisible by 2

    167 ends in 7, so it is odd.

  • Divisible by 3

    The digit sum 14 is not a multiple of 3.

  • Divisible by 4

    The last two digits 67 are not divisible by 4.

  • Divisible by 5

    167 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

    167 does not end in 0.

  • Divisible by 11

    The alternating digit sum 2 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 167 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 167 breaks down

167 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 10100111 supports bitwise reasoning, hexadecimal A7 aligns with computing notation, and the Roman numeral CLXVII keeps the encyclopedic tradition alive. These attributes make 167 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 167 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (162172) to tune search ranges, and educators feature 167 in worksheets about prime identification. Its binary footprint of length 8 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 167 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 167

Is 167 a prime number?

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

What is the prime factorization of 167?

167 is already prime, so the factorization is simply 167.

How is 167 represented in binary and hexadecimal?

167 converts to 10100111 in binary and A7 in hexadecimal, which are helpful for computer science applications.

Is 167 a perfect square, cube, or triangular number?

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

What are the digit sum and digital root of 167?

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