Question

Find Greatest Common Divisor of 24140 and 16762, using Euclidean algorithm.

Answer

The GCD of given numbers is 34.

Explanation

Step 1 :
Divide $24140$ by $16762$ and get the remainder

24140 : 16762 = 1 ( remainder is 7378)

The remainder is positive ( $7378 > 0$ ), so we will continue with division.

Step 2 :
Divide $16762$ by $7378$ and get the remainder

16762 : 7378 = 2 ( remainder is 2006)

The remainder is still positive ( $2006 > 0$ ), so we will continue with division.

Step 3 :
Divide $7378$ by $2006$ and get the remainder

7378 : 2006 = 3 ( remainder is 1360)

The remainder is still positive ( $1360 > 0$ ), so we will continue with division.

Step 4 :
Divide $2006$ by $1360$ and get the remainder

2006 : 1360 = 1 ( remainder is 646)

The remainder is still positive ( $646 > 0$ ), so we will continue with division.

Step 5 :
Divide $1360$ by $646$ and get the remainder

1360 : 646 = 2 ( remainder is 68)

The remainder is still positive ( $68 > 0$ ), so we will continue with division.

Step 6 :
Divide $646$ by $68$ and get the remainder

646 : 68 = 9 ( remainder is 34)

The remainder is still positive ( $34 > 0$ ), so we will continue with division.

Step 7 :
Divide $68$ by $34$ and get the remainder

68 : 34 = 2 ( remainder is 0)

The remainder is zero => GCD is the last divisor $34$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

24140

16762

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

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