Question

Find Greatest Common Divisor of 960 and 112, using Euclidean algorithm.

Answer

The GCD of given numbers is 16.

Explanation

Step 1 :
Divide $960$ by $112$ and get the remainder

960 : 112 = 8 ( remainder is 64)

The remainder is positive ( $64 > 0$ ), so we will continue with division.

Step 2 :
Divide $112$ by $64$ and get the remainder

112 : 64 = 1 ( remainder is 48)

The remainder is still positive ( $48 > 0$ ), so we will continue with division.

Step 3 :
Divide $64$ by $48$ and get the remainder

64 : 48 = 1 ( remainder is 16)

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

Step 4 :
Divide $48$ by $16$ and get the remainder

48 : 16 = 3 ( remainder is 0)

The remainder is zero => GCD is the last divisor $16$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

960

112

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

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