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Prime Number

677

677 is a odd prime number that follows 676 and precedes 678. As a prime number, 677 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 677. 677 is classified as a deficient number based on the sum of its proper divisors. In computer science, 677 is represented as 1010100101 in binary and 2A5 in hexadecimal. Historically, it is written as DCLXXVII in Roman numerals.

Roman Numeral
DCLXXVII
LatinClassic
Binary
1010100101
Base 2
Hexadecimal
2A5
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count3
Digit Sum20
Digital Root2
Sum of Factors678
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

677 is prime, so its only factors are 1 and 677.

Canonical form
677
677
Divisibility Insights
  • Divisible by 2

    677 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 77 are not divisible by 4.

  • Divisible by 5

    677 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

    677 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 677 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 677 breaks down

677 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 1010100101 supports bitwise reasoning, hexadecimal 2A5 aligns with computing notation, and the Roman numeral DCLXXVII keeps the encyclopedic tradition alive. These attributes make 677 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 677 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (672682) to tune search ranges, and educators feature 677 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 677 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 677

Is 677 a prime number?

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

What is the prime factorization of 677?

677 is already prime, so the factorization is simply 677.

How is 677 represented in binary and hexadecimal?

677 converts to 1010100101 in binary and 2A5 in hexadecimal, which are helpful for computer science applications.

Is 677 a perfect square, cube, or triangular number?

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

What are the digit sum and digital root of 677?

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