Suppose we had two numbers a and b, and we did the division algorithm to get a = bq + r for some q , r that belong to Z. (1) Show that if d is a common divisor of b and r, then d is a common divisor of a and b. What does this say about the relationship between (a; b) and (b; r)? (2) Show that if d is a common divisor of a and b, then d is a common divisor of b and r. What does this say about the relationship between (b; r) and (a; b)? (3) Show that (a; b) = (b; r).