Question

Find Greatest Common Divisor of 841 and 160, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $841$ by $160$ and get the remainder

841 : 160 = 5 ( remainder is 41)

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

Step 2 :
Divide $160$ by $41$ and get the remainder

160 : 41 = 3 ( remainder is 37)

The remainder is still positive ( $37 > 0$ ), so we will continue with division.

Step 3 :
Divide $41$ by $37$ and get the remainder

41 : 37 = 1 ( remainder is 4)

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

Step 4 :
Divide $37$ by $4$ and get the remainder

37 : 4 = 9 ( remainder is 1)

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

Step 5 :
Divide $4$ by $1$ and get the remainder

4 : 1 = 4 ( 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

841

160

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

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