Thought provoking questions

1. Real Numbers

1)    Do you find any difference between Euclid division Algorithm and Euclid division Lemma? What difference do you find?

2)    Is there any similarity between division Algorithm and Euclid division algorithm? If so What?

3)    Can we apply Fundamental theorem or Arithmetic to find LCM/GCD of given numbers? If so how?

4)    Is there any difference between an irrational number and a surd?