Question

Find Greatest Common Divisor of 48 and 31, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $48$ by $31$ and get the remainder

48 : 31 = 1 ( remainder is 17)

The remainder is positive ( $17 > 0$ ), so we will continue with division.

Step 2 :
Divide $31$ by $17$ and get the remainder

31 : 17 = 1 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 3 :
Divide $17$ by $14$ and get the remainder

17 : 14 = 1 ( remainder is 3)

The remainder is still positive ( $3 > 0$ ), so we will continue with division.

Step 4 :
Divide $14$ by $3$ and get the remainder

14 : 3 = 4 ( remainder is 2)

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

Step 5 :
Divide $3$ by $2$ and get the remainder

3 : 2 = 1 ( remainder is 1)

The remainder is still positive ( $1 > 0$ ), so we will continue with division.

Step 6 :
Divide $2$ by $1$ and get the remainder

2 : 1 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $1$ .

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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