The best way to examine a solution is to start off with the 'Options' tab and select 'a few steps', then increase the number of steps as additional steps makes the solution process clearer.  Then click on a particular solution step and review the logic which is provided. 

The use of prime factorization does ensure that cancellations are properly recognized and its use can be viewed as a "best practice". For example, when working with fractions it is not immediately obvious that "91/28" has any cancellations at all, while the prime-factored version, "(7 * 13) / (2*2 * 7)", has an obvious cancellation of sevens.  In the problem you provided you will notice that '10' is converted to '2*5' and '12' is converted to '(2^2)*3'.