Question

Find Greatest Common Divisor of 657 and 143, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $657$ by $143$ and get the remainder

657 : 143 = 4 ( remainder is 85)

The remainder is positive ( $85 > 0$ ), so we will continue with division.

Step 2 :
Divide $143$ by $85$ and get the remainder

143 : 85 = 1 ( remainder is 58)

The remainder is still positive ( $58 > 0$ ), so we will continue with division.

Step 3 :
Divide $85$ by $58$ and get the remainder

85 : 58 = 1 ( remainder is 27)

The remainder is still positive ( $27 > 0$ ), so we will continue with division.

Step 4 :
Divide $58$ by $27$ and get the remainder

58 : 27 = 2 ( remainder is 4)

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

Step 5 :
Divide $27$ by $4$ and get the remainder

27 : 4 = 6 ( remainder is 3)

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

Step 6 :
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 7 :
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

657

143

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

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