N
NumberPedia
Menu

© 2025 NumberPedia

Prime Number

659

659 is a odd prime number that follows 658 and precedes 660. As a prime number, 659 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 659. 659 is classified as a deficient number based on the sum of its proper divisors. In computer science, 659 is represented as 1010010011 in binary and 293 in hexadecimal. Historically, it is written as DCLIX in Roman numerals.

Roman Numeral
DCLIX
LatinClassic
Binary
1010010011
Base 2
Hexadecimal
293
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count3
Digit Sum20
Digital Root2
Sum of Factors660
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

659 is prime, so its only factors are 1 and 659.

Canonical form
659
659
Divisibility Insights
  • Divisible by 2

    659 ends in 9, so it is odd.

  • Divisible by 3

    The digit sum 20 is not a multiple of 3.

  • Divisible by 4

    The last two digits 59 are not divisible by 4.

  • Divisible by 5

    659 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

    659 does not end in 0.

  • Divisible by 11

    The alternating digit sum 10 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 659 within several notable number theory sequences:

Prime numbersDeficient numbers
Advertisement

Deep dive

How 659 breaks down

659 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 1010010011 supports bitwise reasoning, hexadecimal 293 aligns with computing notation, and the Roman numeral DCLIX keeps the encyclopedic tradition alive. These attributes make 659 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 659 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (654664) to tune search ranges, and educators feature 659 in worksheets about prime identification. Its binary footprint of length 10 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 659 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 659

Is 659 a prime number?

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

What is the prime factorization of 659?

659 is already prime, so the factorization is simply 659.

How is 659 represented in binary and hexadecimal?

659 converts to 1010010011 in binary and 293 in hexadecimal, which are helpful for computer science applications.

Is 659 a perfect square, cube, or triangular number?

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

What are the digit sum and digital root of 659?

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