Question

Find Greatest Common Divisor of 1874 and 602, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $1874$ by $602$ and get the remainder

1874 : 602 = 3 ( remainder is 68)

The remainder is positive ( $68 > 0$ ), so we will continue with division.

Step 2 :
Divide $602$ by $68$ and get the remainder

602 : 68 = 8 ( remainder is 58)

The remainder is still positive ( $58 > 0$ ), so we will continue with division.

Step 3 :
Divide $68$ by $58$ and get the remainder

68 : 58 = 1 ( remainder is 10)

The remainder is still positive ( $10 > 0$ ), so we will continue with division.

Step 4 :
Divide $58$ by $10$ and get the remainder

58 : 10 = 5 ( remainder is 8)

The remainder is still positive ( $8 > 0$ ), so we will continue with division.

Step 5 :
Divide $10$ by $8$ and get the remainder

10 : 8 = 1 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 6 :
Divide $8$ by $2$ and get the remainder

8 : 2 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

1874

602

937

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

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