Question

Find Greatest Common Divisor of 471 and 562, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 :
Divide $562$ by $471$ and get the remainder

562 : 471 = 1 ( remainder is 91)

The remainder is positive ( $91 > 0$ ), so we will continue with division.

Step 2 :
Divide $471$ by $91$ and get the remainder

471 : 91 = 5 ( remainder is 16)

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

Step 3 :
Divide $91$ by $16$ and get the remainder

91 : 16 = 5 ( remainder is 11)

The remainder is still positive ( $11 > 0$ ), so we will continue with division.

Step 4 :
Divide $16$ by $11$ and get the remainder

16 : 11 = 1 ( remainder is 5)

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

Step 5 :
Divide $11$ by $5$ and get the remainder

11 : 5 = 2 ( remainder is 1)

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

Step 6 :
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

471

562

157

281

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

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