The Euclid's algorithm (also known as the Euclidean Algorithm) is a method for calculating the greatest common divisor (GCD) of two numbers quickly. The Euclidean algorithm is one of the most often used algorithms. It is mentioned in Euclid's Elements (c. 300 BC).
The largest integer that divides both X and Y is the GCD of two integers X and Y. (without leaving a remainder). The greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), and highest common divisor are all terms for the same thing.
The Euclidean algorithm is based on the notion that when the larger number is replaced by its difference with the smaller number, the greatest common divisor of the two integers does not change.
Answers & Comments
Answer:
How can Euclidean algorithm be used to find GCD of two numbers?
1.The Euclidean Algorithm for finding GCD(A,B) is as follows:
2. If A = 0 then GCD(A,B)=B, since the GCD(0,B)=B, and we can stop.
3. If B = 0 then GCD(A,B)=A, since the GCD(A,0)=A, and we can stop.
4. Write A in quotient remainder form (A = B⋅Q + R)
5. Find GCD(B,R) using the Euclidean Algorithm since GCD(A,B) = GCD(B,R)
Calculating LCM of Two Numbers Using a Euclidean Algorithm
1. If a = 0 or b = 0, then return with lcm(a, b) = 0, else go to step 2.
2. Calculate absolute values of the two numbers.
3. Initialize lcm as the higher of the two values computed in step 2.
4. If lcm is divisible by the lower absolute value, then return.
Answer:
The Euclid's algorithm (also known as the Euclidean Algorithm) is a method for calculating the greatest common divisor (GCD) of two numbers quickly. The Euclidean algorithm is one of the most often used algorithms. It is mentioned in Euclid's Elements (c. 300 BC).
The largest integer that divides both X and Y is the GCD of two integers X and Y. (without leaving a remainder). The greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), and highest common divisor are all terms for the same thing.
The Euclidean algorithm is based on the notion that when the larger number is replaced by its difference with the smaller number, the greatest common divisor of the two integers does not change.
Step-by-step explanation:
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