Question

Find Greatest Common Divisor of 868 and 378, using Euclidean algorithm.

Answer

The GCD of given numbers is 14.

Explanation

Step 1 :
Divide $868$ by $378$ and get the remainder

868 : 378 = 2 ( remainder is 112)

The remainder is positive ( $112 > 0$ ), so we will continue with division.

Step 2 :
Divide $378$ by $112$ and get the remainder

378 : 112 = 3 ( remainder is 42)

The remainder is still positive ( $42 > 0$ ), so we will continue with division.

Step 3 :
Divide $112$ by $42$ and get the remainder

112 : 42 = 2 ( remainder is 28)

The remainder is still positive ( $28 > 0$ ), so we will continue with division.

Step 4 :
Divide $42$ by $28$ and get the remainder

42 : 28 = 1 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 5 :
Divide $28$ by $14$ and get the remainder

28 : 14 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $14$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

868

378

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

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