Exercise

Coprime number sequence

Two numbers \(a\) and \(b\) are coprime if their Greatest Common Divisor (GCD) is 1. GCD is the largest positive number that divides two given numbers \(a\) and \(b\). For example, the numbers 7 and 9 are coprime because their GCD is 1.

Given two lists list1 and list2, your task is to create a new list coprimes that contains all the coprime pairs from list1 and list2.

But first, you need to write a function for the GCD using the following algorithm:

  1. check if \(b = 0\)
    • if true, return \(a\) as the GCD between \(a\) and \(b\)
    • if false, go to step 2
  2. make a substitution \(a \leftarrow b\) and \(b \leftarrow a \% b\)
  3. go back to step 1

Instructions 1/2

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  • Define the while loop as described in the context.
  • Complete the return statement.