8.7.6. Running Time of the Euclid GCD Algorithm

Try these first

1. 1.

   Define GCD.

   Hint

   Think about common divisors.

2. 2.

   What is Euclid's algorithm used for?

   Hint

   Consider its historical context.

3. 3.

   What does GCD stand for?

   • Greatest Common Divisor
   • Greatest Common Denominator
   • General Common Divisor

   Hint

   It’s related to division.

4. 4.

   True or False: Euclid's algorithm is less efficient than naive primality testing.

   • True
   • False

   Hint

   Think about their performance with large numbers.

5. 5.

   Using Euclid's algorithm, calculate the GCD of 252 and 105, and discuss how each division step leads to the conclusion.

   Hint

   Follow the division steps closely.

6. 6.

   Using Lame’s theorem, determine how many iterations are needed if the second number is a Fibonacci number.

   Hint

   Consider Fibonacci relationships.