What is the minimum number of divisions made by Euclid’s algorithmamong all inputs 1 ≤ m, n ≤ 10?b. What is the maximum number of divisions made by Euclid’s algorithmamong all inputs 1 ≤ m, n ≤ 10?
Question
What is the minimum number of divisions made by Euclid’s algorithmamong all inputs 1 ≤ m, n ≤ 10?b. What is the maximum number of divisions made by Euclid’s algorithmamong all inputs 1 ≤ m, n ≤ 10?
Solution
a. The minimum number of divisions made by Euclid’s algorithm among all inputs 1 ≤ m, n ≤ 10 is 1. This occurs when one of the numbers is a multiple of the other.
b. The maximum number of divisions made by Euclid’s algorithm among all inputs 1 ≤ m, n ≤ 10 is 6. This occurs for the inputs (m, n) = (10, 7).
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