Question

Find Greatest Common Divisor of 4131 and 2431, using Euclidean algorithm.

Answer

The GCD of given numbers is 17.

Explanation

Step 1 :
Divide $4131$ by $2431$ and get the remainder

4131 : 2431 = 1 ( remainder is 1700)

The remainder is positive ( $1700 > 0$ ), so we will continue with division.

Step 2 :
Divide $2431$ by $1700$ and get the remainder

2431 : 1700 = 1 ( remainder is 731)

The remainder is still positive ( $731 > 0$ ), so we will continue with division.

Step 3 :
Divide $1700$ by $731$ and get the remainder

1700 : 731 = 2 ( remainder is 238)

The remainder is still positive ( $238 > 0$ ), so we will continue with division.

Step 4 :
Divide $731$ by $238$ and get the remainder

731 : 238 = 3 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 5 :
Divide $238$ by $17$ and get the remainder

238 : 17 = 14 ( remainder is 0)

The remainder is zero => GCD is the last divisor $17$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

4131

2431

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

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