Question

Find Greatest Common Divisor of 3094 and 819, using Euclidean algorithm.

Answer

The GCD of given numbers is 91.

Explanation

Step 1 :
Divide $3094$ by $819$ and get the remainder

3094 : 819 = 3 ( remainder is 637)

The remainder is positive ( $637 > 0$ ), so we will continue with division.

Step 2 :
Divide $819$ by $637$ and get the remainder

819 : 637 = 1 ( remainder is 182)

The remainder is still positive ( $182 > 0$ ), so we will continue with division.

Step 3 :
Divide $637$ by $182$ and get the remainder

637 : 182 = 3 ( remainder is 91)

The remainder is still positive ( $91 > 0$ ), so we will continue with division.

Step 4 :
Divide $182$ by $91$ and get the remainder

182 : 91 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $91$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

3094

819

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

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