Question

Find Greatest Common Divisor of 101 and 3267, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $3267$ by $101$ and get the remainder

3267 : 101 = 32 ( remainder is 35)

The remainder is positive ( $35 > 0$ ), so we will continue with division.

Step 2 :
Divide $101$ by $35$ and get the remainder

101 : 35 = 2 ( remainder is 31)

The remainder is still positive ( $31 > 0$ ), so we will continue with division.

Step 3 :
Divide $35$ by $31$ and get the remainder

35 : 31 = 1 ( remainder is 4)

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

Step 4 :
Divide $31$ by $4$ and get the remainder

31 : 4 = 7 ( remainder is 3)

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

Step 5 :
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 6 :
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

101

3267

101

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

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