Question

Find Greatest Common Divisor of 682 and 496, using Euclidean algorithm.

Answer

The GCD of given numbers is 62.

Explanation

Step 1 :
Divide $682$ by $496$ and get the remainder

682 : 496 = 1 ( remainder is 186)

The remainder is positive ( $186 > 0$ ), so we will continue with division.

Step 2 :
Divide $496$ by $186$ and get the remainder

496 : 186 = 2 ( remainder is 124)

The remainder is still positive ( $124 > 0$ ), so we will continue with division.

Step 3 :
Divide $186$ by $124$ and get the remainder

186 : 124 = 1 ( remainder is 62)

The remainder is still positive ( $62 > 0$ ), so we will continue with division.

Step 4 :
Divide $124$ by $62$ and get the remainder

124 : 62 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $62$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

682

496

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

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