Question

Find Greatest Common Divisor of 72 and 47, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $72$ by $47$ and get the remainder

72 : 47 = 1 ( remainder is 25)

The remainder is positive ( $25 > 0$ ), so we will continue with division.

Step 2 :
Divide $47$ by $25$ and get the remainder

47 : 25 = 1 ( remainder is 22)

The remainder is still positive ( $22 > 0$ ), so we will continue with division.

Step 3 :
Divide $25$ by $22$ and get the remainder

25 : 22 = 1 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 4 :
Divide $22$ by $3$ and get the remainder

22 : 3 = 7 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 5 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

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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