Question

Find Greatest Common Divisor of 192 and 258, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $258$ by $192$ and get the remainder

258 : 192 = 1 ( remainder is 66)

The remainder is positive ( $66 > 0$ ), so we will continue with division.

Step 2 :
Divide $192$ by $66$ and get the remainder

192 : 66 = 2 ( remainder is 60)

The remainder is still positive ( $60 > 0$ ), so we will continue with division.

Step 3 :
Divide $66$ by $60$ and get the remainder

66 : 60 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 4 :
Divide $60$ by $6$ and get the remainder

60 : 6 = 10 ( remainder is 0)

The remainder is zero => GCD is the last divisor $6$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

192

258

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

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