Question

Find Greatest Common Divisor of 54 and 98, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $98$ by $54$ and get the remainder

98 : 54 = 1 ( remainder is 44)

The remainder is positive ( $44 > 0$ ), so we will continue with division.

Step 2 :
Divide $54$ by $44$ and get the remainder

54 : 44 = 1 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 3 :
Divide $44$ by $10$ and get the remainder

44 : 10 = 4 ( remainder is 4)

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

Step 4 :
Divide $10$ by $4$ and get the remainder

10 : 4 = 2 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 5 :
Divide $4$ by $2$ and get the remainder

4 : 2 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

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

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