Question

Find Greatest Common Divisor of 130 and 221, using Euclidean algorithm.

Answer

The GCD of given numbers is 13.

Explanation

Step 1 :
Divide $221$ by $130$ and get the remainder

221 : 130 = 1 ( remainder is 91)

The remainder is positive ( $91 > 0$ ), so we will continue with division.

Step 2 :
Divide $130$ by $91$ and get the remainder

130 : 91 = 1 ( remainder is 39)

The remainder is still positive ( $39 > 0$ ), so we will continue with division.

Step 3 :
Divide $91$ by $39$ and get the remainder

91 : 39 = 2 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 4 :
Divide $39$ by $13$ and get the remainder

39 : 13 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $13$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

130

221

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

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