Question

Find Greatest Common Divisor of 81 and 51, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $81$ by $51$ and get the remainder

81 : 51 = 1 ( remainder is 30)

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

Step 2 :
Divide $51$ by $30$ and get the remainder

51 : 30 = 1 ( remainder is 21)

The remainder is still positive ( $21 > 0$ ), so we will continue with division.

Step 3 :
Divide $30$ by $21$ and get the remainder

30 : 21 = 1 ( remainder is 9)

The remainder is still positive ( $9 > 0$ ), so we will continue with division.

Step 4 :
Divide $21$ by $9$ and get the remainder

21 : 9 = 2 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 5 :
Divide $9$ by $3$ and get the remainder

9 : 3 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

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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