Question

Find Greatest Common Divisor of 816 and 2260, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $2260$ by $816$ and get the remainder

2260 : 816 = 2 ( remainder is 628)

The remainder is positive ( $628 > 0$ ), so we will continue with division.

Step 2 :
Divide $816$ by $628$ and get the remainder

816 : 628 = 1 ( remainder is 188)

The remainder is still positive ( $188 > 0$ ), so we will continue with division.

Step 3 :
Divide $628$ by $188$ and get the remainder

628 : 188 = 3 ( remainder is 64)

The remainder is still positive ( $64 > 0$ ), so we will continue with division.

Step 4 :
Divide $188$ by $64$ and get the remainder

188 : 64 = 2 ( remainder is 60)

The remainder is still positive ( $60 > 0$ ), so we will continue with division.

Step 5 :
Divide $64$ by $60$ and get the remainder

64 : 60 = 1 ( remainder is 4)

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

Step 6 :
Divide $60$ by $4$ and get the remainder

60 : 4 = 15 ( 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

816

2260

113

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

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