Question

Find Greatest Common Divisor of 6897 and 11857, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $11857$ by $6897$ and get the remainder

11857 : 6897 = 1 ( remainder is 4960)

The remainder is positive ( $4960 > 0$ ), so we will continue with division.

Step 2 :
Divide $6897$ by $4960$ and get the remainder

6897 : 4960 = 1 ( remainder is 1937)

The remainder is still positive ( $1937 > 0$ ), so we will continue with division.

Step 3 :
Divide $4960$ by $1937$ and get the remainder

4960 : 1937 = 2 ( remainder is 1086)

The remainder is still positive ( $1086 > 0$ ), so we will continue with division.

Step 4 :
Divide $1937$ by $1086$ and get the remainder

1937 : 1086 = 1 ( remainder is 851)

The remainder is still positive ( $851 > 0$ ), so we will continue with division.

Step 5 :
Divide $1086$ by $851$ and get the remainder

1086 : 851 = 1 ( remainder is 235)

The remainder is still positive ( $235 > 0$ ), so we will continue with division.

Step 6 :
Divide $851$ by $235$ and get the remainder

851 : 235 = 3 ( remainder is 146)

The remainder is still positive ( $146 > 0$ ), so we will continue with division.

Step 7 :
Divide $235$ by $146$ and get the remainder

235 : 146 = 1 ( remainder is 89)

The remainder is still positive ( $89 > 0$ ), so we will continue with division.

Step 8 :
Divide $146$ by $89$ and get the remainder

146 : 89 = 1 ( remainder is 57)

The remainder is still positive ( $57 > 0$ ), so we will continue with division.

Step 9 :
Divide $89$ by $57$ and get the remainder

89 : 57 = 1 ( remainder is 32)

The remainder is still positive ( $32 > 0$ ), so we will continue with division.

Step 10 :
Divide $57$ by $32$ and get the remainder

57 : 32 = 1 ( remainder is 25)

The remainder is still positive ( $25 > 0$ ), so we will continue with division.

Step 11 :
Divide $32$ by $25$ and get the remainder

32 : 25 = 1 ( remainder is 7)

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

Step 12 :
Divide $25$ by $7$ and get the remainder

25 : 7 = 3 ( remainder is 4)

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

Step 13 :
Divide $7$ by $4$ and get the remainder

7 : 4 = 1 ( remainder is 3)

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

Step 14 :
Divide $4$ by $3$ and get the remainder

4 : 3 = 1 ( remainder is 1)

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

Step 15 :
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

6897

11857

167

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

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