Question

Find Greatest Common Divisor of 232 and 562, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $562$ by $232$ and get the remainder

562 : 232 = 2 ( remainder is 98)

The remainder is positive ( $98 > 0$ ), so we will continue with division.

Step 2 :
Divide $232$ by $98$ and get the remainder

232 : 98 = 2 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 3 :
Divide $98$ by $36$ and get the remainder

98 : 36 = 2 ( remainder is 26)

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

Step 4 :
Divide $36$ by $26$ and get the remainder

36 : 26 = 1 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 5 :
Divide $26$ by $10$ and get the remainder

26 : 10 = 2 ( remainder is 6)

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

Step 6 :
Divide $10$ by $6$ and get the remainder

10 : 6 = 1 ( remainder is 4)

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

Step 7 :
Divide $6$ by $4$ and get the remainder

6 : 4 = 1 ( remainder is 2)

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

Step 8 :
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

232

562

281

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

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