Question

Find Greatest Common Divisor of 407 and 1010, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1010$ by $407$ and get the remainder

1010 : 407 = 2 ( remainder is 196)

The remainder is positive ( $196 > 0$ ), so we will continue with division.

Step 2 :
Divide $407$ by $196$ and get the remainder

407 : 196 = 2 ( remainder is 15)

The remainder is still positive ( $15 > 0$ ), so we will continue with division.

Step 3 :
Divide $196$ by $15$ and get the remainder

196 : 15 = 13 ( remainder is 1)

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

Step 4 :
Divide $15$ by $1$ and get the remainder

15 : 1 = 15 ( 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

407

1010

101

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

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