12. Euclidean Domains (SLASH) PID (SLASH) UFD Overview

Euclidean Algorithms — Quiz

Test your understanding of euclidean algorithms with 5 practice questions.

Practice Questions

Question 1

What is the main idea of the Euclidean algorithm for integers?

Question 2

When applying the Euclidean algorithm to find the greatest common divisor of $84$ and $30$, what is the remainder when $84$ is divided by $30$?

Question 3

In the Euclidean algorithm, what does the last nonzero remainder equal?

Question 4

Why does the Euclidean algorithm always terminate for positive integers?

Question 5

In a division step $a=bq+r$ with $b>0$, what condition must $r$ satisfy?