Question

Find Greatest Common Divisor of 114 and 312, using Euclidean algorithm.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 :
Divide $312$ by $114$ and get the remainder

312 : 114 = 2 ( remainder is 84)

The remainder is positive ( $84 > 0$ ), so we will continue with division.

Step 2 :
Divide $114$ by $84$ and get the remainder

114 : 84 = 1 ( remainder is 30)

The remainder is still positive ( $30 > 0$ ), so we will continue with division.

Step 3 :
Divide $84$ by $30$ and get the remainder

84 : 30 = 2 ( remainder is 24)

The remainder is still positive ( $24 > 0$ ), so we will continue with division.

Step 4 :
Divide $30$ by $24$ and get the remainder

30 : 24 = 1 ( remainder is 6)

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

Step 5 :
Divide $24$ by $6$ and get the remainder

24 : 6 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $6$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

114

312

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

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