Question

Find Greatest Common Divisor of 442 and 1120, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $1120$ by $442$ and get the remainder

1120 : 442 = 2 ( remainder is 236)

The remainder is positive ( $236 > 0$ ), so we will continue with division.

Step 2 :
Divide $442$ by $236$ and get the remainder

442 : 236 = 1 ( remainder is 206)

The remainder is still positive ( $206 > 0$ ), so we will continue with division.

Step 3 :
Divide $236$ by $206$ and get the remainder

236 : 206 = 1 ( remainder is 30)

The remainder is still positive ( $30 > 0$ ), so we will continue with division.

Step 4 :
Divide $206$ by $30$ and get the remainder

206 : 30 = 6 ( remainder is 26)

The remainder is still positive ( $26 > 0$ ), so we will continue with division.

Step 5 :
Divide $30$ by $26$ and get the remainder

30 : 26 = 1 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 6 :
Divide $26$ by $4$ and get the remainder

26 : 4 = 6 ( remainder is 2)

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

Step 7 :
Divide $4$ by $2$ and get the remainder

4 : 2 = 2 ( 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

442

1120

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

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