Question

Find Greatest Common Divisor of 132 and 630, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $630$ by $132$ and get the remainder

630 : 132 = 4 ( remainder is 102)

The remainder is positive ( $102 > 0$ ), so we will continue with division.

Step 2 :
Divide $132$ by $102$ and get the remainder

132 : 102 = 1 ( remainder is 30)

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

Step 3 :
Divide $102$ by $30$ and get the remainder

102 : 30 = 3 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 4 :
Divide $30$ by $12$ and get the remainder

30 : 12 = 2 ( remainder is 6)

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

Step 5 :
Divide $12$ by $6$ and get the remainder

12 : 6 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $6$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

132

630

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

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