Question

Find Greatest Common Divisor of 332 and 192, using Euclidean algorithm.

Answer

The GCD of given numbers is 4.

Explanation

Step 1 :
Divide $332$ by $192$ and get the remainder

332 : 192 = 1 ( remainder is 140)

The remainder is positive ( $140 > 0$ ), so we will continue with division.

Step 2 :
Divide $192$ by $140$ and get the remainder

192 : 140 = 1 ( remainder is 52)

The remainder is still positive ( $52 > 0$ ), so we will continue with division.

Step 3 :
Divide $140$ by $52$ and get the remainder

140 : 52 = 2 ( remainder is 36)

The remainder is still positive ( $36 > 0$ ), so we will continue with division.

Step 4 :
Divide $52$ by $36$ and get the remainder

52 : 36 = 1 ( remainder is 16)

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

Step 5 :
Divide $36$ by $16$ and get the remainder

36 : 16 = 2 ( remainder is 4)

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

Step 6 :
Divide $16$ by $4$ and get the remainder

16 : 4 = 4 ( 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

332

192

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

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