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GCD Euclidean Algorithm
GCD Euclidean Algorithm
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1)
What does GCD stand for?
Greatest Common Denominator
Greatest Common Difference
Greatest Common Divisor
Greatest Common Distributor
2)
What is the GCD Euclidean Algorithm?
A method for finding the greatest common divisor of two integers
A method for finding the greatest common factor of two integers
A method for finding the least common multiple of two integers
A method for finding the smallest common multiple of two integers
3)
What is the purpose of the GCD Euclidean Algorithm?
To identify the prime numbers in a given set
To calculate the greatest common factor of two integers
To calculate the greatest common divisor of two integers
To calculate the least common multiple of two integers
4)
How does the GCD Euclidean Algorithm work?
By repeatedly subtracting the smaller number from the larger number until the two numbers are equal
By repeatedly multiplying the two numbers together until the result is 1
By repeatedly adding the two numbers together until the result is 0
By repeatedly dividing the larger number by the smaller number until the remainder is 0
5)
The Euclidean algorithm runs efficiently if the remainder of two numbers is divided by the minimum of two numbers until the remainder is zero.
True
False
6)
What is the total running time of Euclid’s algorithm?
O(N log N)
O(N)
O(N log M)
O(log N +1)
7)
What is the formula for Euclidean algorithm?
GCD (m,n,o,p) = GCD (m, m mod n, o, p mod o)
LCM (m,n,o,p) = LCM (m, m mod n, o, p mod o)
LCM (m,n) = LCM (n, m mod n)
GCD (m,n) = GCD (n, m mod n)
8)
What is the total running time of the binary GCD algorithm?
O(log N)
O(N)
O(N log N)
O(N²)
9)
What is the GCD of 20 and 12 using Euclid’s algorithm?
2
8
4
6
10)
Which of the following is not an application of Euclidean algorithm
Solving quadratic equations
Performing division in modular arithmetic
Simplification of fraction
Solving Diophantine equations
