Question

Find Greatest Common Divisor of 118 and 25, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $118$ by $25$ and get the remainder

118 : 25 = 4 ( remainder is 18)

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

Step 2 :
Divide $25$ by $18$ and get the remainder

25 : 18 = 1 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 3 :
Divide $18$ by $7$ and get the remainder

18 : 7 = 2 ( remainder is 4)

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

Step 4 :
Divide $7$ by $4$ and get the remainder

7 : 4 = 1 ( remainder is 3)

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

Step 5 :
Divide $4$ by $3$ and get the remainder

4 : 3 = 1 ( remainder is 1)

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

Step 6 :
Divide $3$ by $1$ and get the remainder

3 : 1 = 3 ( 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

118

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

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