Question

Find Greatest Common Divisor of 72 and 44, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $72$ by $44$ and get the remainder

72 : 44 = 1 ( remainder is 28)

The remainder is positive ( $28 > 0$ ), so we will continue with division.

Step 2 :
Divide $44$ by $28$ and get the remainder

44 : 28 = 1 ( remainder is 16)

The remainder is still positive ( $16 > 0$ ), so we will continue with division.

Step 3 :
Divide $28$ by $16$ and get the remainder

28 : 16 = 1 ( remainder is 12)

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

Step 4 :
Divide $16$ by $12$ and get the remainder

16 : 12 = 1 ( remainder is 4)

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

Step 5 :
Divide $12$ by $4$ and get the remainder

12 : 4 = 3 ( 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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