Question

Find Greatest Common Divisor of 2947 and 3997, using Euclidean algorithm.

Answer

The GCD of given numbers is 7.

Explanation

Step 1 :
Divide $3997$ by $2947$ and get the remainder

3997 : 2947 = 1 ( remainder is 1050)

The remainder is positive ( $1050 > 0$ ), so we will continue with division.

Step 2 :
Divide $2947$ by $1050$ and get the remainder

2947 : 1050 = 2 ( remainder is 847)

The remainder is still positive ( $847 > 0$ ), so we will continue with division.

Step 3 :
Divide $1050$ by $847$ and get the remainder

1050 : 847 = 1 ( remainder is 203)

The remainder is still positive ( $203 > 0$ ), so we will continue with division.

Step 4 :
Divide $847$ by $203$ and get the remainder

847 : 203 = 4 ( remainder is 35)

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

Step 5 :
Divide $203$ by $35$ and get the remainder

203 : 35 = 5 ( remainder is 28)

The remainder is still positive ( $28 > 0$ ), so we will continue with division.

Step 6 :
Divide $35$ by $28$ and get the remainder

35 : 28 = 1 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 7 :
Divide $28$ by $7$ and get the remainder

28 : 7 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $7$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2947

3997

421

571

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

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