Question

Find Greatest Common Divisor of 2957 and 400680, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $400680$ by $2957$ and get the remainder

400680 : 2957 = 135 ( remainder is 1485)

The remainder is positive ( $1485 > 0$ ), so we will continue with division.

Step 2 :
Divide $2957$ by $1485$ and get the remainder

2957 : 1485 = 1 ( remainder is 1472)

The remainder is still positive ( $1472 > 0$ ), so we will continue with division.

Step 3 :
Divide $1485$ by $1472$ and get the remainder

1485 : 1472 = 1 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 4 :
Divide $1472$ by $13$ and get the remainder

1472 : 13 = 113 ( remainder is 3)

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

Step 5 :
Divide $13$ by $3$ and get the remainder

13 : 3 = 4 ( 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

2957

400680

2957

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

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