Question

Find Greatest Common Divisor of 457 and 378, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $457$ by $378$ and get the remainder

457 : 378 = 1 ( remainder is 79)

The remainder is positive ( $79 > 0$ ), so we will continue with division.

Step 2 :
Divide $378$ by $79$ and get the remainder

378 : 79 = 4 ( remainder is 62)

The remainder is still positive ( $62 > 0$ ), so we will continue with division.

Step 3 :
Divide $79$ by $62$ and get the remainder

79 : 62 = 1 ( remainder is 17)

The remainder is still positive ( $17 > 0$ ), so we will continue with division.

Step 4 :
Divide $62$ by $17$ and get the remainder

62 : 17 = 3 ( remainder is 11)

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

Step 5 :
Divide $17$ by $11$ and get the remainder

17 : 11 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 6 :
Divide $11$ by $6$ and get the remainder

11 : 6 = 1 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 7 :
Divide $6$ by $5$ and get the remainder

6 : 5 = 1 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 8 :
Divide $5$ by $1$ and get the remainder

5 : 1 = 5 ( 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

457

378

457

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

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