Question

Find Greatest Common Divisor of 82 and 60, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $82$ by $60$ and get the remainder

82 : 60 = 1 ( remainder is 22)

The remainder is positive ( $22 > 0$ ), so we will continue with division.

Step 2 :
Divide $60$ by $22$ and get the remainder

60 : 22 = 2 ( remainder is 16)

The remainder is still positive ( $16 > 0$ ), so we will continue with division.

Step 3 :
Divide $22$ by $16$ and get the remainder

22 : 16 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 4 :
Divide $16$ by $6$ and get the remainder

16 : 6 = 2 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 5 :
Divide $6$ by $4$ and get the remainder

6 : 4 = 1 ( remainder is 2)

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

Step 6 :
Divide $4$ by $2$ and get the remainder

4 : 2 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

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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