Question

Find Greatest Common Divisor of 792 and 275, using Euclidean algorithm.

Answer

The GCD of given numbers is 11.

Explanation

Step 1 :
Divide $792$ by $275$ and get the remainder

792 : 275 = 2 ( remainder is 242)

The remainder is positive ( $242 > 0$ ), so we will continue with division.

Step 2 :
Divide $275$ by $242$ and get the remainder

275 : 242 = 1 ( remainder is 33)

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

Step 3 :
Divide $242$ by $33$ and get the remainder

242 : 33 = 7 ( remainder is 11)

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

Step 4 :
Divide $33$ by $11$ and get the remainder

33 : 11 = 3 ( 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

792

275

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

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