(Solved): division and euclidean algorithm \( 3(6 \mathrm{pts}) \) Apply the non-recursive division algorithm ...

\( 3(6 \mathrm{pts}) \) Apply the non-recursive division algorithm to find the quotient and remainder when 83 is divided by 7 . Show all steps (diagram carefully). \[ x=83 \quad v=7 \] quotient remainder 4 (6 pts) Use the extended Euclidean algorithm (using matrices) to find integers \( s \) and \( t \) such that \( 81 s+11 t=\operatorname{gcd}(81,11 \) ) (show all steps). \[ a=81, \quad b=11 \] If \( a \) and \( b \) are two \( n \)-bit numbers, what is a good bound for the number of iterations of the loop in the algorithm? \[ O(\log n) \quad O(n) \quad O(n \log n) \quad O\left(n^{2}\right) \]