Question

Find Greatest Common Divisor of 44 and 70, using Euclidean algorithm.

Answer

The GCD of given numbers is 2.

Explanation

Step 1 :
Divide $70$ by $44$ and get the remainder

70 : 44 = 1 ( remainder is 26)

The remainder is positive ( $26 > 0$ ), so we will continue with division.

Step 2 :
Divide $44$ by $26$ and get the remainder

44 : 26 = 1 ( remainder is 18)

The remainder is still positive ( $18 > 0$ ), so we will continue with division.

Step 3 :
Divide $26$ by $18$ and get the remainder

26 : 18 = 1 ( remainder is 8)

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

Step 4 :
Divide $18$ by $8$ and get the remainder

18 : 8 = 2 ( remainder is 2)

The remainder is still positive ( $2 > 0$ ), so we will continue with division.

Step 5 :
Divide $8$ by $2$ and get the remainder

8 : 2 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $2$ .

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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