Question

Find Greatest Common Divisor of 3532 and 3288, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $3532$ by $3288$ and get the remainder

3532 : 3288 = 1 ( remainder is 244)

The remainder is positive ( $244 > 0$ ), so we will continue with division.

Step 2 :
Divide $3288$ by $244$ and get the remainder

3288 : 244 = 13 ( remainder is 116)

The remainder is still positive ( $116 > 0$ ), so we will continue with division.

Step 3 :
Divide $244$ by $116$ and get the remainder

244 : 116 = 2 ( remainder is 12)

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

Step 4 :
Divide $116$ by $12$ and get the remainder

116 : 12 = 9 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 5 :
Divide $12$ by $8$ and get the remainder

12 : 8 = 1 ( remainder is 4)

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

Step 6 :
Divide $8$ by $4$ and get the remainder

8 : 4 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $4$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

3532

3288

883

137

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

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