Question

Find Greatest Common Divisor of 634 and 472, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $634$ by $472$ and get the remainder

634 : 472 = 1 ( remainder is 162)

The remainder is positive ( $162 > 0$ ), so we will continue with division.

Step 2 :
Divide $472$ by $162$ and get the remainder

472 : 162 = 2 ( remainder is 148)

The remainder is still positive ( $148 > 0$ ), so we will continue with division.

Step 3 :
Divide $162$ by $148$ and get the remainder

162 : 148 = 1 ( remainder is 14)

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

Step 4 :
Divide $148$ by $14$ and get the remainder

148 : 14 = 10 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 5 :
Divide $14$ by $8$ and get the remainder

14 : 8 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 6 :
Divide $8$ by $6$ and get the remainder

8 : 6 = 1 ( remainder is 2)

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

Step 7 :
Divide $6$ by $2$ and get the remainder

6 : 2 = 3 ( 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

634

472

317

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

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