Question

Find Greatest Common Divisor of 1001 and 100001, using Euclidean algorithm.

Answer

The GCD of given numbers is 11.

Explanation

Step 1 :
Divide $100001$ by $1001$ and get the remainder

100001 : 1001 = 99 ( remainder is 902)

The remainder is positive ( $902 > 0$ ), so we will continue with division.

Step 2 :
Divide $1001$ by $902$ and get the remainder

1001 : 902 = 1 ( remainder is 99)

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

Step 3 :
Divide $902$ by $99$ and get the remainder

902 : 99 = 9 ( remainder is 11)

The remainder is still positive ( $11 > 0$ ), so we will continue with division.

Step 4 :
Divide $99$ by $11$ and get the remainder

99 : 11 = 9 ( remainder is 0)

The remainder is zero => GCD is the last divisor $11$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1001

100001

9091

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

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