Question

Find Greatest Common Divisor of 5880420 and 229, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $5880420$ by $229$ and get the remainder

5880420 : 229 = 25678 ( remainder is 158)

The remainder is positive ( $158 > 0$ ), so we will continue with division.

Step 2 :
Divide $229$ by $158$ and get the remainder

229 : 158 = 1 ( remainder is 71)

The remainder is still positive ( $71 > 0$ ), so we will continue with division.

Step 3 :
Divide $158$ by $71$ and get the remainder

158 : 71 = 2 ( remainder is 16)

The remainder is still positive ( $16 > 0$ ), so we will continue with division.

Step 4 :
Divide $71$ by $16$ and get the remainder

71 : 16 = 4 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 5 :
Divide $16$ by $7$ and get the remainder

16 : 7 = 2 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 6 :
Divide $7$ by $2$ and get the remainder

7 : 2 = 3 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 7 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

5880420

229

359

229

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

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