Question

Find Greatest Common Divisor of 710 and 310, using Euclidean algorithm.

Answer

The GCD of given numbers is 10.

Explanation

Step 1 :
Divide $710$ by $310$ and get the remainder

710 : 310 = 2 ( remainder is 90)

The remainder is positive ( $90 > 0$ ), so we will continue with division.

Step 2 :
Divide $310$ by $90$ and get the remainder

310 : 90 = 3 ( remainder is 40)

The remainder is still positive ( $40 > 0$ ), so we will continue with division.

Step 3 :
Divide $90$ by $40$ and get the remainder

90 : 40 = 2 ( remainder is 10)

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

Step 4 :
Divide $40$ by $10$ and get the remainder

40 : 10 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $10$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

710

310

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

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