Question

Find Greatest Common Divisor of 857 and 239, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $857$ by $239$ and get the remainder

857 : 239 = 3 ( remainder is 140)

The remainder is positive ( $140 > 0$ ), so we will continue with division.

Step 2 :
Divide $239$ by $140$ and get the remainder

239 : 140 = 1 ( remainder is 99)

The remainder is still positive ( $99 > 0$ ), so we will continue with division.

Step 3 :
Divide $140$ by $99$ and get the remainder

140 : 99 = 1 ( remainder is 41)

The remainder is still positive ( $41 > 0$ ), so we will continue with division.

Step 4 :
Divide $99$ by $41$ and get the remainder

99 : 41 = 2 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 5 :
Divide $41$ by $17$ and get the remainder

41 : 17 = 2 ( remainder is 7)

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

Step 6 :
Divide $17$ by $7$ and get the remainder

17 : 7 = 2 ( remainder is 3)

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

Step 7 :
Divide $7$ by $3$ and get the remainder

7 : 3 = 2 ( remainder is 1)

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

Step 8 :
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

857

239

857

239

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

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