5. This question is based on material in Section 4.10 Application: Algorithms of the course textbook.

(a) Construct a trace table to trace the action of Algorithm 4.10.1 Division Algorithm for the input variables a = 5852 and d = 1302, and state the output of the algorithm.

(b) Construct a trace table to trace the action of Algorithm 4.10.2 Euclidean Algorithm for the input variables 5852 and 1302, and state the output of the algorithm.

(c) Algorithm 4.10.3 Computing gcd's by Subtraction provides an alternative to the Euclidean Algorithm, and is described in Question 27 of the end of section exercises.

(i) Construct a trace table of the first seven iterations of Algorithm 4.10.3 for the input variables 5852 and 1302 (do not complete the algorithm).

(ii) How many iterations would it take for Algorithm 4.10.3 to complete the calculation of the gcd of 5852 and 1302?