Shor's Algorithm: Quantum Factoring Explained

In this video, we show how quantum computers can factor large numbers.

Note that the table that follows the slides that discuss the 4 different scenarios for the possible values of the primes p and q correctly summarizes the findings in the discussion in these slides. However, there are typos in the intermediate steps in these slides in the equations for GCD(a,N) and GCD(b,N). To elaborate:

For scenario #1: GCD(b, N)=1 (i.e. it is NOT equal to a_ia_j, since we are assuming in this scenario that N and b have no common factors).
For scenario #2: It should be: GCD(a,N)=a_i=p, and GCD(b,N)=b_j=q.
For scenario #3: It should be: GCD(a,N)=a_j=q , and GCD(b,N)=b_i=p.
For scenario #4: GCD(a, N)=1 (i.e. it is NOT equal to b_ib_j, since we are assuming in this scenario that N and a have no common factors).