Question

Find Greatest Common Divisor of 43650 and 4980, using Euclidean algorithm.

Answer

The GCD of given numbers is 30.

Explanation

Step 1 :
Divide $43650$ by $4980$ and get the remainder

43650 : 4980 = 8 ( remainder is 3810)

The remainder is positive ( $3810 > 0$ ), so we will continue with division.

Step 2 :
Divide $4980$ by $3810$ and get the remainder

4980 : 3810 = 1 ( remainder is 1170)

The remainder is still positive ( $1170 > 0$ ), so we will continue with division.

Step 3 :
Divide $3810$ by $1170$ and get the remainder

3810 : 1170 = 3 ( remainder is 300)

The remainder is still positive ( $300 > 0$ ), so we will continue with division.

Step 4 :
Divide $1170$ by $300$ and get the remainder

1170 : 300 = 3 ( remainder is 270)

The remainder is still positive ( $270 > 0$ ), so we will continue with division.

Step 5 :
Divide $300$ by $270$ and get the remainder

300 : 270 = 1 ( remainder is 30)

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

Step 6 :
Divide $270$ by $30$ and get the remainder

270 : 30 = 9 ( remainder is 0)

The remainder is zero => GCD is the last divisor $30$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

43650

4980

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

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