Question

Find Greatest Common Divisor of 359 and 125, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $359$ by $125$ and get the remainder

359 : 125 = 2 ( remainder is 109)

The remainder is positive ( $109 > 0$ ), so we will continue with division.

Step 2 :
Divide $125$ by $109$ and get the remainder

125 : 109 = 1 ( remainder is 16)

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

Step 3 :
Divide $109$ by $16$ and get the remainder

109 : 16 = 6 ( remainder is 13)

The remainder is still positive ( $13 > 0$ ), so we will continue with division.

Step 4 :
Divide $16$ by $13$ and get the remainder

16 : 13 = 1 ( remainder is 3)

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

Step 5 :
Divide $13$ by $3$ and get the remainder

13 : 3 = 4 ( 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

359

125

359

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

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