8.7.5 - Proof of Euclid’s GCD Algorithm
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Practice Questions
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What is the GCD of 15 and 25?
💡 Hint: Find common factors of both numbers.
Is 7 a prime number?
💡 Hint: Check divisibility.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the GCD of 48 and 18?
💡 Hint: Remember to apply the division process.
True or False: All prime numbers are odd except 2.
💡 Hint: Recalling the definition of prime numbers.
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Challenge Problems
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Prove Euclid's algorithm by using a counterexample to show that if GCD(a, b) is the same as GCD(b, r), then the algorithm will function correctly.
💡 Hint: Consider specific values for a and b and their remainders to illustrate your point.
Design an efficient algorithm to compute the GCD of 3 integers using the concept of pairwise GCD.
💡 Hint: Use the associative property of GCD.
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