Question

Find Greatest Common Divisor of 243 and 198, using Euclidean algorithm.

Answer

The GCD of given numbers is 9.

Explanation

Step 1 :
Divide $243$ by $198$ and get the remainder

243 : 198 = 1 ( remainder is 45)

The remainder is positive ( $45 > 0$ ), so we will continue with division.

Step 2 :
Divide $198$ by $45$ and get the remainder

198 : 45 = 4 ( remainder is 18)

The remainder is still positive ( $18 > 0$ ), so we will continue with division.

Step 3 :
Divide $45$ by $18$ and get the remainder

45 : 18 = 2 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 4 :
Divide $18$ by $9$ and get the remainder

18 : 9 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $9$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

243

198

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

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