Question

Find Greatest Common Divisor of 195 and 340, using Euclidean algorithm.

Answer

The GCD of given numbers is 5.

Explanation

Step 1 :
Divide $340$ by $195$ and get the remainder

340 : 195 = 1 ( remainder is 145)

The remainder is positive ( $145 > 0$ ), so we will continue with division.

Step 2 :
Divide $195$ by $145$ and get the remainder

195 : 145 = 1 ( remainder is 50)

The remainder is still positive ( $50 > 0$ ), so we will continue with division.

Step 3 :
Divide $145$ by $50$ and get the remainder

145 : 50 = 2 ( remainder is 45)

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

Step 4 :
Divide $50$ by $45$ and get the remainder

50 : 45 = 1 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 5 :
Divide $45$ by $5$ and get the remainder

45 : 5 = 9 ( remainder is 0)

The remainder is zero => GCD is the last divisor $5$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

195

340

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

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