Question

Find Greatest Common Divisor of 471 and 9231, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $9231$ by $471$ and get the remainder

9231 : 471 = 19 ( remainder is 282)

The remainder is positive ( $282 > 0$ ), so we will continue with division.

Step 2 :
Divide $471$ by $282$ and get the remainder

471 : 282 = 1 ( remainder is 189)

The remainder is still positive ( $189 > 0$ ), so we will continue with division.

Step 3 :
Divide $282$ by $189$ and get the remainder

282 : 189 = 1 ( remainder is 93)

The remainder is still positive ( $93 > 0$ ), so we will continue with division.

Step 4 :
Divide $189$ by $93$ and get the remainder

189 : 93 = 2 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 5 :
Divide $93$ by $3$ and get the remainder

93 : 3 = 31 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

471

9231

157

181

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

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