Question

Find Greatest Common Divisor of 4424 and 864, using Euclidean algorithm.

Answer

The GCD of given numbers is 8.

Explanation

Step 1 :
Divide $4424$ by $864$ and get the remainder

4424 : 864 = 5 ( remainder is 104)

The remainder is positive ( $104 > 0$ ), so we will continue with division.

Step 2 :
Divide $864$ by $104$ and get the remainder

864 : 104 = 8 ( remainder is 32)

The remainder is still positive ( $32 > 0$ ), so we will continue with division.

Step 3 :
Divide $104$ by $32$ and get the remainder

104 : 32 = 3 ( remainder is 8)

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

Step 4 :
Divide $32$ by $8$ and get the remainder

32 : 8 = 4 ( remainder is 0)

The remainder is zero => GCD is the last divisor $8$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

4424

864

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

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