Question

Find Greatest Common Divisor of 2282 and 420, using Euclidean algorithm.

Answer

The GCD of given numbers is 14.

Explanation

Step 1 :
Divide $2282$ by $420$ and get the remainder

2282 : 420 = 5 ( remainder is 182)

The remainder is positive ( $182 > 0$ ), so we will continue with division.

Step 2 :
Divide $420$ by $182$ and get the remainder

420 : 182 = 2 ( remainder is 56)

The remainder is still positive ( $56 > 0$ ), so we will continue with division.

Step 3 :
Divide $182$ by $56$ and get the remainder

182 : 56 = 3 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 4 :
Divide $56$ by $14$ and get the remainder

56 : 14 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $14$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

2282

420

163

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

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