Question

Find Greatest Common Divisor of 196 and 340, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $340$ by $196$ and get the remainder

340 : 196 = 1 ( remainder is 144)

The remainder is positive ( $144 > 0$ ), so we will continue with division.

Step 2 :
Divide $196$ by $144$ and get the remainder

196 : 144 = 1 ( remainder is 52)

The remainder is still positive ( $52 > 0$ ), so we will continue with division.

Step 3 :
Divide $144$ by $52$ and get the remainder

144 : 52 = 2 ( remainder is 40)

The remainder is still positive ( $40 > 0$ ), so we will continue with division.

Step 4 :
Divide $52$ by $40$ and get the remainder

52 : 40 = 1 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 5 :
Divide $40$ by $12$ and get the remainder

40 : 12 = 3 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 6 :
Divide $12$ by $4$ and get the remainder

12 : 4 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $4$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

196

340

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

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