Question

Find Greatest Common Divisor of 1092 and 2295, using Euclidean algorithm.

Answer

The GCD of given numbers is 3.

Explanation

Step 1 :
Divide $2295$ by $1092$ and get the remainder

2295 : 1092 = 2 ( remainder is 111)

The remainder is positive ( $111 > 0$ ), so we will continue with division.

Step 2 :
Divide $1092$ by $111$ and get the remainder

1092 : 111 = 9 ( remainder is 93)

The remainder is still positive ( $93 > 0$ ), so we will continue with division.

Step 3 :
Divide $111$ by $93$ and get the remainder

111 : 93 = 1 ( remainder is 18)

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

Step 4 :
Divide $93$ by $18$ and get the remainder

93 : 18 = 5 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 5 :
Divide $18$ by $3$ and get the remainder

18 : 3 = 6 ( remainder is 0)

The remainder is zero => GCD is the last divisor $3$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1092

2295

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

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