Question

Find Greatest Common Divisor of 16261 and 85652, using Euclidean algorithm.

Answer

The GCD of given numbers is 161.

Explanation

Step 1 :
Divide $85652$ by $16261$ and get the remainder

85652 : 16261 = 5 ( remainder is 4347)

The remainder is positive ( $4347 > 0$ ), so we will continue with division.

Step 2 :
Divide $16261$ by $4347$ and get the remainder

16261 : 4347 = 3 ( remainder is 3220)

The remainder is still positive ( $3220 > 0$ ), so we will continue with division.

Step 3 :
Divide $4347$ by $3220$ and get the remainder

4347 : 3220 = 1 ( remainder is 1127)

The remainder is still positive ( $1127 > 0$ ), so we will continue with division.

Step 4 :
Divide $3220$ by $1127$ and get the remainder

3220 : 1127 = 2 ( remainder is 966)

The remainder is still positive ( $966 > 0$ ), so we will continue with division.

Step 5 :
Divide $1127$ by $966$ and get the remainder

1127 : 966 = 1 ( remainder is 161)

The remainder is still positive ( $161 > 0$ ), so we will continue with division.

Step 6 :
Divide $966$ by $161$ and get the remainder

966 : 161 = 6 ( remainder is 0)

The remainder is zero => GCD is the last divisor $161$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

16261

85652

101

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

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