Question

Find Greatest Common Divisor of 3768 and 1701, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $3768$ by $1701$ and get the remainder

3768 : 1701 = 2 ( remainder is 366)

The remainder is positive ( $366 > 0$ ), so we will continue with division.

Step 2 :
Divide $1701$ by $366$ and get the remainder

1701 : 366 = 4 ( remainder is 237)

The remainder is still positive ( $237 > 0$ ), so we will continue with division.

Step 3 :
Divide $366$ by $237$ and get the remainder

366 : 237 = 1 ( remainder is 129)

The remainder is still positive ( $129 > 0$ ), so we will continue with division.

Step 4 :
Divide $237$ by $129$ and get the remainder

237 : 129 = 1 ( remainder is 108)

The remainder is still positive ( $108 > 0$ ), so we will continue with division.

Step 5 :
Divide $129$ by $108$ and get the remainder

129 : 108 = 1 ( remainder is 21)

The remainder is still positive ( $21 > 0$ ), so we will continue with division.

Step 6 :
Divide $108$ by $21$ and get the remainder

108 : 21 = 5 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 7 :
Divide $21$ by $3$ and get the remainder

21 : 3 = 7 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

3768

1701

157

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

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