Question

Find Greatest Common Divisor of 1315 and 572, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $1315$ by $572$ and get the remainder

1315 : 572 = 2 ( remainder is 171)

The remainder is positive ( $171 > 0$ ), so we will continue with division.

Step 2 :
Divide $572$ by $171$ and get the remainder

572 : 171 = 3 ( remainder is 59)

The remainder is still positive ( $59 > 0$ ), so we will continue with division.

Step 3 :
Divide $171$ by $59$ and get the remainder

171 : 59 = 2 ( remainder is 53)

The remainder is still positive ( $53 > 0$ ), so we will continue with division.

Step 4 :
Divide $59$ by $53$ and get the remainder

59 : 53 = 1 ( remainder is 6)

The remainder is still positive ( $6 > 0$ ), so we will continue with division.

Step 5 :
Divide $53$ by $6$ and get the remainder

53 : 6 = 8 ( remainder is 5)

The remainder is still positive ( $5 > 0$ ), so we will continue with division.

Step 6 :
Divide $6$ by $5$ and get the remainder

6 : 5 = 1 ( remainder is 1)

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

Step 7 :
Divide $5$ by $1$ and get the remainder

5 : 1 = 5 ( 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

1315

572

263

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

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