Question

Find Greatest Common Divisor of 2260 and 812, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $2260$ by $812$ and get the remainder

2260 : 812 = 2 ( remainder is 636)

The remainder is positive ( $636 > 0$ ), so we will continue with division.

Step 2 :
Divide $812$ by $636$ and get the remainder

812 : 636 = 1 ( remainder is 176)

The remainder is still positive ( $176 > 0$ ), so we will continue with division.

Step 3 :
Divide $636$ by $176$ and get the remainder

636 : 176 = 3 ( remainder is 108)

The remainder is still positive ( $108 > 0$ ), so we will continue with division.

Step 4 :
Divide $176$ by $108$ and get the remainder

176 : 108 = 1 ( remainder is 68)

The remainder is still positive ( $68 > 0$ ), so we will continue with division.

Step 5 :
Divide $108$ by $68$ and get the remainder

108 : 68 = 1 ( remainder is 40)

The remainder is still positive ( $40 > 0$ ), so we will continue with division.

Step 6 :
Divide $68$ by $40$ and get the remainder

68 : 40 = 1 ( remainder is 28)

The remainder is still positive ( $28 > 0$ ), so we will continue with division.

Step 7 :
Divide $40$ by $28$ and get the remainder

40 : 28 = 1 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 8 :
Divide $28$ by $12$ and get the remainder

28 : 12 = 2 ( remainder is 4)

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

Step 9 :
Divide $12$ by $4$ and get the remainder

12 : 4 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $4$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2260

812

113

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

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