Question

Find Greatest Common Divisor of 324 and 528, using Euclidean algorithm.

Answer

The GCD of given numbers is 12.

Explanation

Step 1 :
Divide $528$ by $324$ and get the remainder

528 : 324 = 1 ( remainder is 204)

The remainder is positive ( $204 > 0$ ), so we will continue with division.

Step 2 :
Divide $324$ by $204$ and get the remainder

324 : 204 = 1 ( remainder is 120)

The remainder is still positive ( $120 > 0$ ), so we will continue with division.

Step 3 :
Divide $204$ by $120$ and get the remainder

204 : 120 = 1 ( remainder is 84)

The remainder is still positive ( $84 > 0$ ), so we will continue with division.

Step 4 :
Divide $120$ by $84$ and get the remainder

120 : 84 = 1 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 5 :
Divide $84$ by $36$ and get the remainder

84 : 36 = 2 ( remainder is 12)

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

Step 6 :
Divide $36$ by $12$ and get the remainder

36 : 12 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $12$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

324

528

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

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