Question

Find Greatest Common Divisor of 397 and 450, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $450$ by $397$ and get the remainder

450 : 397 = 1 ( remainder is 53)

The remainder is positive ( $53 > 0$ ), so we will continue with division.

Step 2 :
Divide $397$ by $53$ and get the remainder

397 : 53 = 7 ( remainder is 26)

The remainder is still positive ( $26 > 0$ ), so we will continue with division.

Step 3 :
Divide $53$ by $26$ and get the remainder

53 : 26 = 2 ( remainder is 1)

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

Step 4 :
Divide $26$ by $1$ and get the remainder

26 : 1 = 26 ( 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

397

450

397

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

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