Question

Find Greatest Common Divisor of 97 and 63, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $97$ by $63$ and get the remainder

97 : 63 = 1 ( remainder is 34)

The remainder is positive ( $34 > 0$ ), so we will continue with division.

Step 2 :
Divide $63$ by $34$ and get the remainder

63 : 34 = 1 ( remainder is 29)

The remainder is still positive ( $29 > 0$ ), so we will continue with division.

Step 3 :
Divide $34$ by $29$ and get the remainder

34 : 29 = 1 ( remainder is 5)

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

Step 4 :
Divide $29$ by $5$ and get the remainder

29 : 5 = 5 ( remainder is 4)

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

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

5 : 4 = 1 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 6 :
Divide $4$ by $1$ and get the remainder

4 : 1 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

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.

This page was created using

GCD Calculator