Question

Find Greatest Common Divisor of 295 and 504, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $504$ by $295$ and get the remainder

504 : 295 = 1 ( remainder is 209)

The remainder is positive ( $209 > 0$ ), so we will continue with division.

Step 2 :
Divide $295$ by $209$ and get the remainder

295 : 209 = 1 ( remainder is 86)

The remainder is still positive ( $86 > 0$ ), so we will continue with division.

Step 3 :
Divide $209$ by $86$ and get the remainder

209 : 86 = 2 ( remainder is 37)

The remainder is still positive ( $37 > 0$ ), so we will continue with division.

Step 4 :
Divide $86$ by $37$ and get the remainder

86 : 37 = 2 ( remainder is 12)

The remainder is still positive ( $12 > 0$ ), so we will continue with division.

Step 5 :
Divide $37$ by $12$ and get the remainder

37 : 12 = 3 ( remainder is 1)

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

Step 6 :
Divide $12$ by $1$ and get the remainder

12 : 1 = 12 ( 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

295

504

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

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