Practice Introduction (9.1) - Lecture – 57: Properties of GCD and Bezout’s Theorem

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6 sample questions

Question 1.
What is the GCD of 12 and 15?
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List the factors of both numbers.
Question 2.
State Bezout's Theorem in your own words.
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Think about what a linear combination means.
3Question 3.
What does GCD stand for?
- Greatest Common Denominator
- Greatest Common Divisor
- General Combinatorial Division
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Think about what 'divisor' means.
4Question 4.
True or False: Bezout's Theorem requires the integers to be positive.
- True
- False
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Remember that coefficients can be negative.
Question 5.
If a = 198 and b = 252, find the GCD using the Extended Euclidean Algorithm and provide the Bezout coefficients.
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Follow the steps of the Extended Euclidean Algorithm carefully.
Question 6.
Prove that if GCD(a, b) = 1, then a and b are coprime by applying Bezout’s theorem.
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Use the definitions of gcd and linear combinations to show their relationship.

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