Question

Find Greatest Common Divisor of 312 and 518, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $518$ by $312$ and get the remainder

518 : 312 = 1 ( remainder is 206)

The remainder is positive ( $206 > 0$ ), so we will continue with division.

Step 2 :
Divide $312$ by $206$ and get the remainder

312 : 206 = 1 ( remainder is 106)

The remainder is still positive ( $106 > 0$ ), so we will continue with division.

Step 3 :
Divide $206$ by $106$ and get the remainder

206 : 106 = 1 ( remainder is 100)

The remainder is still positive ( $100 > 0$ ), so we will continue with division.

Step 4 :
Divide $106$ by $100$ and get the remainder

106 : 100 = 1 ( remainder is 6)

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

Step 5 :
Divide $100$ by $6$ and get the remainder

100 : 6 = 16 ( remainder is 4)

The remainder is still positive ( $4 > 0$ ), so we will continue with division.

Step 6 :
Divide $6$ by $4$ and get the remainder

6 : 4 = 1 ( remainder is 2)

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

Step 7 :
Divide $4$ by $2$ and get the remainder

4 : 2 = 2 ( 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

312

518

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

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