text: # Euclidean Algorithm/Examples/341 and 527
  
  ## Examples of Use of Euclidean Algorithm
  
  The GCD of $341$ and $527$ is found to be:
  
  $\gcd \set {341, 527} = 31$
  
  ### Integer Combination
  
  $31$ can be expressed as an integer combination of $341$ and $527$:
  
  $31 = 2 \times 527 - 3 \times 341$
  
  ## Proof
  
   $\text {(1)}: \quad$ $\ds 527$ $=$ $\ds 1 \times 341 + 186$ $\text {(2)}: \quad$ $\ds 341$ $=$ $\ds 1 \times 186 + 155$ $\text {(3)}: \quad$ $\ds 186$ $=$ $\ds 1 \times 155 + 31$ $\ds 155$ $=$ $\ds 5 \times 31$
explanation: The document provides an example of the Euclidean Algorithm applied to the numbers 341 and 527. It includes the greatest common divisor (GCD) of these numbers, an integer combination expressing the GCD, and a step-by-step proof of the algorithm. The document does not contain a question but rather a detailed explanation and solution.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Euclidean Algorithm/Examples/341 and 527
  
  ## Examples of Use of Euclidean Algorithm
  
  The GCD of $341$ and $527$ is found to be:
  
  $\gcd \set {341, 527} = 31$
  
  ### Integer Combination
  
  $31$ can be expressed as an integer combination of $341$ and $527$:
  
  $31 = 2 \times 527 - 3 \times 341$
  
  ## Proof
  
   $\text {(1)}: \quad$ $\ds 527$ $=$ $\ds 1 \times 341 + 186$ $\text {(2)}: \quad$ $\ds 341$ $=$ $\ds 1 \times 186 + 155$ $\text {(3)}: \quad$ $\ds 186$ $=$ $\ds 1 \times 155 + 31$ $\ds 155$ $=$ $\ds 5 \times 31$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides an example of the Euclidean Algorithm applied to the numbers 341 and 527. It includes the greatest common divisor (GCD) of these numbers, an integer combination expressing the GCD, and a step-by-step proof of the algorithm. The document does not contain a question but rather a detailed explanation and solution.
  
  Label: no-question