Question

Find Greatest Common Divisor of 2378 and 1764, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $2378$ by $1764$ and get the remainder

2378 : 1764 = 1 ( remainder is 614)

The remainder is positive ( $614 > 0$ ), so we will continue with division.

Step 2 :
Divide $1764$ by $614$ and get the remainder

1764 : 614 = 2 ( remainder is 536)

The remainder is still positive ( $536 > 0$ ), so we will continue with division.

Step 3 :
Divide $614$ by $536$ and get the remainder

614 : 536 = 1 ( remainder is 78)

The remainder is still positive ( $78 > 0$ ), so we will continue with division.

Step 4 :
Divide $536$ by $78$ and get the remainder

536 : 78 = 6 ( remainder is 68)

The remainder is still positive ( $68 > 0$ ), so we will continue with division.

Step 5 :
Divide $78$ by $68$ and get the remainder

78 : 68 = 1 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 6 :
Divide $68$ by $10$ and get the remainder

68 : 10 = 6 ( remainder is 8)

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

Step 7 :
Divide $10$ by $8$ and get the remainder

10 : 8 = 1 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 8 :
Divide $8$ by $2$ and get the remainder

8 : 2 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2378

1764

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

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