# 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

 $\text {(1)}: \quad$ $\ds 527$ $=$ $\ds 1 \times 341 + 186$ $\text {(2)}: \quad$ $\ds 341$ $=$ $\ds 1 \times 186 + 155$ $\text {(3)}: \quad$ $\ds 186$ $=$ $\ds 1 \times 155 + 31$ $\ds 155$ $=$ $\ds 5 \times 31$
The text passage provides a detailed example of the Euclidean Algorithm to find the greatest common divisor (GCD) of 341 and 527, along with a proof and an integer combination expression.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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

 $\text {(1)}: \quad$ $\ds 527$ $=$ $\ds 1 \times 341 + 186$ $\text {(2)}: \quad$ $\ds 341$ $=$ $\ds 1 \times 186 + 155$ $\text {(3)}: \quad$ $\ds 186$ $=$ $\ds 1 \times 155 + 31$ $\ds 155$ $=$ $\ds 5 \times 31$
user
The text passage provides a detailed example of the Euclidean Algorithm to find the greatest common divisor (GCD) of 341 and 527, along with a proof and an integer combination expression.

TYPE: SINGLE_QUESTION_WITH_ANSWER