Final answer:
Euclid's algorithm is used to find the GCD of two numbers by repeatedly dividing the larger number by the smaller and using the remainder as the new divisor, until the remainder is zero. The last non-zero divisor is the GCD.
Step-by-step explanation:
Applying Euclid's Algorithm for GCD
Euclid's algorithm is a method for finding the Greatest Common Divisor (GCD) of two numbers, which is the largest number that divides both of them without leaving a remainder. To apply Euclid's algorithm, you follow these steps:
Given two numbers, identify the larger one (A) and the smaller one (B).
Divide A by B, and note the remainder (R).
Replace A with B and B with R in the algorithm.
Repeat steps 2 and 3 until the remainder (R) is zero. The divisor (B) at this point will be the GCD.
For example, to find the GCD of 48 and 18:
48 ÷ 18 = 2 remainder 12, so A=18 and B=12 now.
18 ÷ 12 = 1 remainder 6, so A=12 and B=6 now.
12 ÷ 6 = 2 remainder 0, we stop here as the remainder is 0.
The last non-zero remainder is 6, so the GCD of 48 and 18 is 6.