Question

Find Greatest Common Divisor of 29106 and 5382, using Euclidean algorithm.

Answer

The GCD of given numbers is 18.

Explanation

Step 1 :
Divide $29106$ by $5382$ and get the remainder

29106 : 5382 = 5 ( remainder is 2196)

The remainder is positive ( $2196 > 0$ ), so we will continue with division.

Step 2 :
Divide $5382$ by $2196$ and get the remainder

5382 : 2196 = 2 ( remainder is 990)

The remainder is still positive ( $990 > 0$ ), so we will continue with division.

Step 3 :
Divide $2196$ by $990$ and get the remainder

2196 : 990 = 2 ( remainder is 216)

The remainder is still positive ( $216 > 0$ ), so we will continue with division.

Step 4 :
Divide $990$ by $216$ and get the remainder

990 : 216 = 4 ( remainder is 126)

The remainder is still positive ( $126 > 0$ ), so we will continue with division.

Step 5 :
Divide $216$ by $126$ and get the remainder

216 : 126 = 1 ( remainder is 90)

The remainder is still positive ( $90 > 0$ ), so we will continue with division.

Step 6 :
Divide $126$ by $90$ and get the remainder

126 : 90 = 1 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 7 :
Divide $90$ by $36$ and get the remainder

90 : 36 = 2 ( remainder is 18)

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

Step 8 :
Divide $36$ by $18$ and get the remainder

36 : 18 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $18$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

29106

5382

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

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