Question

Find Greatest Common Divisor of 3210 and 1108, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $3210$ by $1108$ and get the remainder

3210 : 1108 = 2 ( remainder is 994)

The remainder is positive ( $994 > 0$ ), so we will continue with division.

Step 2 :
Divide $1108$ by $994$ and get the remainder

1108 : 994 = 1 ( remainder is 114)

The remainder is still positive ( $114 > 0$ ), so we will continue with division.

Step 3 :
Divide $994$ by $114$ and get the remainder

994 : 114 = 8 ( remainder is 82)

The remainder is still positive ( $82 > 0$ ), so we will continue with division.

Step 4 :
Divide $114$ by $82$ and get the remainder

114 : 82 = 1 ( remainder is 32)

The remainder is still positive ( $32 > 0$ ), so we will continue with division.

Step 5 :
Divide $82$ by $32$ and get the remainder

82 : 32 = 2 ( remainder is 18)

The remainder is still positive ( $18 > 0$ ), so we will continue with division.

Step 6 :
Divide $32$ by $18$ and get the remainder

32 : 18 = 1 ( remainder is 14)

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

Step 7 :
Divide $18$ by $14$ and get the remainder

18 : 14 = 1 ( remainder is 4)

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

Step 8 :
Divide $14$ by $4$ and get the remainder

14 : 4 = 3 ( 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

3210

1108

107

277

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

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