Question

Find Greatest Common Divisor of 1147 and 889, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1147$ by $889$ and get the remainder

1147 : 889 = 1 ( remainder is 258)

The remainder is positive ( $258 > 0$ ), so we will continue with division.

Step 2 :
Divide $889$ by $258$ and get the remainder

889 : 258 = 3 ( remainder is 115)

The remainder is still positive ( $115 > 0$ ), so we will continue with division.

Step 3 :
Divide $258$ by $115$ and get the remainder

258 : 115 = 2 ( remainder is 28)

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

Step 4 :
Divide $115$ by $28$ and get the remainder

115 : 28 = 4 ( remainder is 3)

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

Step 5 :
Divide $28$ by $3$ and get the remainder

28 : 3 = 9 ( remainder is 1)

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

Step 6 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( 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

1147

889

127

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

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