Question

Find Greatest Common Divisor of 3158 and 1226, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $3158$ by $1226$ and get the remainder

3158 : 1226 = 2 ( remainder is 706)

The remainder is positive ( $706 > 0$ ), so we will continue with division.

Step 2 :
Divide $1226$ by $706$ and get the remainder

1226 : 706 = 1 ( remainder is 520)

The remainder is still positive ( $520 > 0$ ), so we will continue with division.

Step 3 :
Divide $706$ by $520$ and get the remainder

706 : 520 = 1 ( remainder is 186)

The remainder is still positive ( $186 > 0$ ), so we will continue with division.

Step 4 :
Divide $520$ by $186$ and get the remainder

520 : 186 = 2 ( remainder is 148)

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

Step 5 :
Divide $186$ by $148$ and get the remainder

186 : 148 = 1 ( remainder is 38)

The remainder is still positive ( $38 > 0$ ), so we will continue with division.

Step 6 :
Divide $148$ by $38$ and get the remainder

148 : 38 = 3 ( remainder is 34)

The remainder is still positive ( $34 > 0$ ), so we will continue with division.

Step 7 :
Divide $38$ by $34$ and get the remainder

38 : 34 = 1 ( remainder is 4)

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

Step 8 :
Divide $34$ by $4$ and get the remainder

34 : 4 = 8 ( remainder is 2)

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

Step 9 :
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

3158

1226

1579

613

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

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