Question

Find Greatest Common Divisor of 72 and 52, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $72$ by $52$ and get the remainder

72 : 52 = 1 ( remainder is 20)

The remainder is positive ( $20 > 0$ ), so we will continue with division.

Step 2 :
Divide $52$ by $20$ and get the remainder

52 : 20 = 2 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 3 :
Divide $20$ by $12$ and get the remainder

20 : 12 = 1 ( remainder is 8)

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

Step 4 :
Divide $12$ by $8$ and get the remainder

12 : 8 = 1 ( remainder is 4)

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

Step 5 :
Divide $8$ by $4$ and get the remainder

8 : 4 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $4$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

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

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