Question

Find Greatest Common Divisor of 67 and 37, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $67$ by $37$ and get the remainder

67 : 37 = 1 ( remainder is 30)

The remainder is positive ( $30 > 0$ ), so we will continue with division.

Step 2 :
Divide $37$ by $30$ and get the remainder

37 : 30 = 1 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 3 :
Divide $30$ by $7$ and get the remainder

30 : 7 = 4 ( remainder is 2)

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

Step 4 :
Divide $7$ by $2$ and get the remainder

7 : 2 = 3 ( remainder is 1)

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

Step 5 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( 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.

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