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Question

Find Greatest Common Divisor of 128 and 64, using Euclidean algorithm.

Answer

The GCD of given numbers is 64.

Explanation

Step 1 :
Divide $ 128 $ by $ 64 $ and get the remainder

$$ 128 : \color{blue}{ \boxed { 64 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 64 }} $.

We can summarize an algorithm into a following table.

128 : 64 = 2 remainder ( 0 )
GCD = 64

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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