Question

Find Greatest Common Divisor of 442 and 272, using Euclidean algorithm.

Answer

The GCD of given numbers is 34.

Explanation

Step 1 :
Divide $442$ by $272$ and get the remainder

442 : 272 = 1 ( remainder is 170)

The remainder is positive ( $170 > 0$ ), so we will continue with division.

Step 2 :
Divide $272$ by $170$ and get the remainder

272 : 170 = 1 ( remainder is 102)

The remainder is still positive ( $102 > 0$ ), so we will continue with division.

Step 3 :
Divide $170$ by $102$ and get the remainder

170 : 102 = 1 ( remainder is 68)

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

Step 4 :
Divide $102$ by $68$ and get the remainder

102 : 68 = 1 ( remainder is 34)

The remainder is still positive ( $34 > 0$ ), so we will continue with division.

Step 5 :
Divide $68$ by $34$ and get the remainder

68 : 34 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $34$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

442

272

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

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