Question

Find Greatest Common Divisor of 3850 and 1162, using Euclidean algorithm.

Answer

The GCD of given numbers is 14.

Explanation

Step 1 :
Divide $3850$ by $1162$ and get the remainder

3850 : 1162 = 3 ( remainder is 364)

The remainder is positive ( $364 > 0$ ), so we will continue with division.

Step 2 :
Divide $1162$ by $364$ and get the remainder

1162 : 364 = 3 ( remainder is 70)

The remainder is still positive ( $70 > 0$ ), so we will continue with division.

Step 3 :
Divide $364$ by $70$ and get the remainder

364 : 70 = 5 ( remainder is 14)

The remainder is still positive ( $14 > 0$ ), so we will continue with division.

Step 4 :
Divide $70$ by $14$ and get the remainder

70 : 14 = 5 ( remainder is 0)

The remainder is zero => GCD is the last divisor $14$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

3850

1162

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

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