Question

Find Greatest Common Divisor of 462 and 357, using Euclidean algorithm.

Answer

The GCD of given numbers is 21.

Explanation

Step 1 :
Divide $462$ by $357$ and get the remainder

462 : 357 = 1 ( remainder is 105)

The remainder is positive ( $105 > 0$ ), so we will continue with division.

Step 2 :
Divide $357$ by $105$ and get the remainder

357 : 105 = 3 ( remainder is 42)

The remainder is still positive ( $42 > 0$ ), so we will continue with division.

Step 3 :
Divide $105$ by $42$ and get the remainder

105 : 42 = 2 ( remainder is 21)

The remainder is still positive ( $21 > 0$ ), so we will continue with division.

Step 4 :
Divide $42$ by $21$ and get the remainder

42 : 21 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $21$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

462

357

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

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