Question

Find Greatest Common Divisor of 385 and 1188, using Euclidean algorithm.

Answer

The GCD of given numbers is 11.

Explanation

Step 1 :
Divide $1188$ by $385$ and get the remainder

1188 : 385 = 3 ( remainder is 33)

The remainder is positive ( $33 > 0$ ), so we will continue with division.

Step 2 :
Divide $385$ by $33$ and get the remainder

385 : 33 = 11 ( remainder is 22)

The remainder is still positive ( $22 > 0$ ), so we will continue with division.

Step 3 :
Divide $33$ by $22$ and get the remainder

33 : 22 = 1 ( remainder is 11)

The remainder is still positive ( $11 > 0$ ), so we will continue with division.

Step 4 :
Divide $22$ by $11$ and get the remainder

22 : 11 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $11$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

385

1188

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

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