Question

Find Greatest Common Divisor of 52598 and 2541, using Euclidean algorithm.

Answer

The GCD of given numbers is 7.

Explanation

Step 1 :
Divide $52598$ by $2541$ and get the remainder

52598 : 2541 = 20 ( remainder is 1778)

The remainder is positive ( $1778 > 0$ ), so we will continue with division.

Step 2 :
Divide $2541$ by $1778$ and get the remainder

2541 : 1778 = 1 ( remainder is 763)

The remainder is still positive ( $763 > 0$ ), so we will continue with division.

Step 3 :
Divide $1778$ by $763$ and get the remainder

1778 : 763 = 2 ( remainder is 252)

The remainder is still positive ( $252 > 0$ ), so we will continue with division.

Step 4 :
Divide $763$ by $252$ and get the remainder

763 : 252 = 3 ( remainder is 7)

The remainder is still positive ( $7 > 0$ ), so we will continue with division.

Step 5 :
Divide $252$ by $7$ and get the remainder

252 : 7 = 36 ( remainder is 0)

The remainder is zero => GCD is the last divisor $7$ .

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

0,0

52598

2541

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

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